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Mathematical model of ferromagnetism in statistical mechanics
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical
Ising_model
Mathematical model of magnetism
The transverse field Ising model is a quantum version of the classical Ising model. It features a lattice with nearest neighbour interactions determined
Transverse-field_Ising_model
Model in statistical mechanics
square lattice Ising model is a simple lattice model of interacting magnetic spins, an example of the class of Ising models. The model is notable for
Square_lattice_Ising_model
German physicist (1900–1998)
Ernst Ising (German: [ˈiːzɪŋ]; May 10, 1900 – May 11, 1998) was a German physicist, who is best remembered for the development of the Ising model. He was
Ernst_Ising
Collection of models with the same renormalization group flow limit
exponents are the same for all models in the class. Well-studied examples include the universality classes of the Ising model or the percolation theory at
Universality_class
Model in statistical physics
The Ising model is a prototypical model in statistical physics. The model consists of discrete variables that represent magnetic dipole moments of atomic
High-dimensional_Ising_model
Conformal field theory of the 2D Ising model critical point
The two-dimensional critical Ising model is the critical limit of the Ising model in two dimensions. It is a two-dimensional conformal field theory whose
Two-dimensional critical Ising model
Two-dimensional_critical_Ising_model
Deliberately simplistic scientific model
IS–LM model, the Mundell–Fleming model, the RBC model, and the New Keynesian model. Examples of toy models in physics include: the Ising model as a toy
Toy_model
Science that understands human crowds
physics is the relationship of the Ising model and the voting dynamics of a finite population. The Ising model, as a model of ferromagnetism, is represented
Social_physics
Approximation of physical behavior
some simple cases (e.g. certain Gaussian random-field theories, the 1D Ising model). Often combinatorial problems arise that make things like computing
Mean-field_theory
Ensemble of states at a constant temperature
solutions in some interacting model systems. A classic example of this is the Ising model, which is a widely discussed toy model for the phenomena of ferromagnetism
Canonical_ensemble
Statistical model in quantum mechanics of magnetic materials
are treated quantum mechanically. It is related to the prototypical Ising model, where at each site of a lattice, a spin σ i ∈ { ± 1 } {\displaystyle
Quantum_Heisenberg_model
Type of random graph
etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random
Random_cluster_model
Physical model defined on a lattice
Examples of exactly solvable models are the periodic 1D Ising model, and the periodic 2D Ising model with vanishing external magnetic field, H = 0 , {\displaystyle
Lattice_model_(physics)
Model in statistical mechanics generalizing the Ising model
the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain
Potts_model
Type of stochastic recurrent neural network
Sherrington–Kirkpatrick model with external field or stochastic Ising model), named after Ludwig Boltzmann, is a spin-glass model with an external field
Boltzmann_machine
Lattice model of statistical mechanics
\beta }} Hence the critical β of the XY model cannot be smaller than the double of the critical β of the Ising model β c X Y ≥ 2 β c I s {\displaystyle \beta
Classical_XY_model
Physics associated with critical points
to explain the physical origin of these phenomena, we shall use the Ising model as a pedagogical example. Consider a 2 D {\displaystyle 2D} square array
Critical_phenomena
Temperature above which magnetic properties change
electrons in the structure and here the Ising model can predict their behaviour with each other. This model is important for solving and understanding
Curie_temperature
Symmetry in statistical physics
energy of a two-dimensional square-lattice Ising model at a low temperature to that of another Ising model at a high temperature. It was discovered by
Kramers–Wannier_duality
Mathematical model
chosen randomly from some specified probability distribution. The 1D Ising model of spin glass is usually written as H = − ∑ i = 1 N J i , i + 1 S i S
NK_model
Statistical mechanics model for phase transitions
transitions. Originally developed for the Ising model, the theory has been extended and applied to a wide range of models and phenomena, including protein folding
Lee–Yang_theory
Norwegian-American physical chemist and theoretical physicist (1903-1976)
1D Ising model, which was already solved by Ising himself. He then computed the transfer matrix of the "Ising ladder", meaning two 1D Ising models side-by-side
Lars_Onsager
Combinatorial optimization problem
learning models include support-vector machines, clustering and probabilistic graphical models. Moreover, due to its close connection to Ising models, QUBO
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Disordered magnetic state
limit of very small external fields. The Edwards-Anderson model is similar to the Ising model, in which spins are arranged on a d {\displaystyle d} -dimensional
Spin_glass
Quantum field theory enjoying conformal symmetry
tensor operator).[citation needed] The critical Ising model is the critical point of the Ising model on a hypercubic lattice in two or three dimensions
Conformal_field_theory
Class of artificial neural network
statistical mechanics. The Ising model was developed by Wilhelm Lenz and Ernst Ising in the 1920s as a simple statistical mechanical model of magnets at equilibrium
Recurrent_neural_network
Form of artificial neural network
of associative memory was statistical mechanics. The Ising model was published in 1920s as a model of magnetism, however it studied the thermal equilibrium
Hopfield_network
Physical process of transition between basic states of matter
antimonide. A simplified but highly useful model of magnetic phase transitions is provided by the Ising model. Phase transitions involving solutions and
Phase_transition
Parameter describing physics near critical points
dimensions or when exact solutions are known such as the two-dimensional Ising model. The theoretical treatment in generic dimensions requires the renormalization
Critical_exponent
Features that do not change if length or energy scales are multiplied by a common factor
the Ising model lattice. So this anomalous dimension in the conformal field theory is the same as a particular critical exponent of the Ising model phase
Scale_invariance
statistical mechanics. The Ising model was developed by Wilhelm Lenz and Ernst Ising in the 1920s as a simple statistical mechanical model of magnets at equilibrium
History of artificial neural networks
History_of_artificial_neural_networks
Mathematical model used to explain magnetism
the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles)
Spin_model
Quantum physics-based metaheuristic for optimization problems
system is expected to have reached the ground state of the classical Ising model that corresponds to the solution to the original optimization problem
Quantum_annealing
Regular pattern of magnetic moment ordering
redirect targets Ising model – Mathematical model of ferromagnetism in statistical mechanics ANNNI model – Variant of the Ising model Mottness – Materials
Antiferromagnetism
Surname list
physicist Jane Ising (1902–2012), German-American economist Rudolf Ising (1903–1992), American animator Ising model, mathematical model of ferromagnetism
Ising
Representation of a type of random process
In statistics, an autoregressive (AR) model is a modelled representation of a type of random process. It can be used to describe time-varying processes
Autoregressive_model
Criterion in mean field theory
through measurable quantities, such as the magnetic susceptibility in the Ising model. It also gives the idea of an upper critical dimension, a dimensionality
Ginzburg_criterion
Variant of the Ising model
anisotropic) next-nearest neighbor Ising model, usually known as the ANNNI model, is a variant of the Ising model. In the ANNNI model, competing ferromagnetic and
ANNNI_model
Quantum mechanical effect
form of Eq. (14) corresponds identically to the Ising model of ferromagnetism except that in the Ising model, the dot product of the two spin angular momenta
Exchange_interaction
Agent-based segregation model
fundamental dynamics of the agents resemble the mechanics used in the Ising model of ferromagnetism. This primarily relies on the similar nature in which
Schelling's model of segregation
Schelling's_model_of_segregation
Theorem in statistical mechanics
proved for the Ising model by T. D. Lee and C. N. Yang (1952) (Lee & Yang 1952). Their result was later extended to more general models by several people
Lee–Yang_theorem
Cognitive science approach
networks had precursors in the Ising model due to Wilhelm Lenz (1920) and Ernst Ising (1925), though the Ising model conceived by them did not involve
Connectionism
Concept in statistical physics
correlations decay algebraically. Quantum Heisenberg model Quantum rotor model Ising model Classical XY model Magnetism Ferromagnetism Landau–Lifshitz equation
Classical_Heisenberg_model
Algebraic encoding of graph connectivity
partition function of the ferromagnetic Ising model. This exploits the close connection between the Ising model and the problem of counting matchings in
Tutte_polynomial
Eugene Stanley as a generalization of the Ising model, XY model and Heisenberg model. In the n-vector model, n-component unit-length classical spins s
N-vector_model
Algorithm in statistical physics
In statistical physics, Glauber dynamics is a way to simulate the Ising model (a model of magnetism) on a computer . The algorithm is named after Roy J
Glauber_dynamics
Doubling map on the unit interval
and modular forms. The Hamiltonian of the zero-field one-dimensional Ising model of 2 N {\displaystyle 2N} spins with periodic boundary conditions can
Dyadic_transformation
Set of random variables
Markov random field is the Ising model; indeed, the Markov random field was introduced as the general setting for the Ising model. In the domain of artificial
Markov_random_field
{\displaystyle Z_{N}} model (also known as the clock model) is a simplified statistical mechanical spin model. It is a generalization of the Ising model. Although
ZN_model
Dependence of the state of a system on its history
critical state model (magnetism) Bouc–Wen model (structural engineering) Ising model (magnetism) Jiles–Atherton model (magnetism) Novak–Tyson model (cell-cycle
Hysteresis
Mathematical concept
the model's Z 2 {\displaystyle \mathbb {Z} _{2}} symmetry. An example of the Markov property can be seen in the Gibbs measure of the Ising model. The
Gibbs_measure
the Ising model. There are many dynamical rules for the Ising model where the steady state is Gibbsian. The 2-dimensional ferromagnetic Ising model in
Toom's_rule
Core of an atom composed of nucleons
cluster models are the 1936 resonating group structure model of John Wheeler, close-packed spheron model of Linus Pauling and the 2D Ising model of MacGregor
Atomic_nucleus
Generalization of the ice-type (six-vertex) models
eight-vertex model, and the (2,4)-spin Ising model. Consequently a solution in either model would lead immediately to a solution in the other. Six-vertex model Transfer-matrix
Eight-vertex_model
Model of magnetic susceptibility under certain conditions
terms corresponding to the interaction among the pairs of the atom. Ising model is one of the simplest approximations of such pairwise interaction. H
Curie–Weiss_law
Mathematical model for a quantum system
(neglecting Coulomb forces). The model differs from similar spin-models such as the Ising model and the Heisenberg model in that it includes a term analogous
Quantum_rotor_model
Computer that uses photons or light waves
Ising machines are computers whose design was inspired by the theoretical Ising model. Yoshihisa Yamamoto's lab at Stanford pioneered building Ising machines
Optical_computing
Property of certain dynamical systems
are examples. 8-vertex model Ice-type model of Lieb Gaudin model Ising model in 1- and 2-dimensions ZN model (or clock model) in 1- and 2-dimensions
Integrable_system
Anglo-Australian physicist (1924–2000)
developments "often without knowing it, and generally without quoting him." The Ising model was another one of his research interests. In 1955, Ward was recruited
John_Clive_Ward
ixu(n,N)).} Recall that the partition function of the one-dimensional Ising model can be defined as follows. Fix N ≥ 1 {\displaystyle N\geq 1} representing
Rudin–Shapiro_sequence
Quantum field theory with four-point interactions
{\displaystyle \phi ^{4}} model belongs to the Griffiths-Simon class, meaning that it can be represented also as the weak limit of an Ising model on a certain type
Quartic_interaction
Branch of machine learning
whereas FNNs do not. In the 1920s, Wilhelm Lenz and Ernst Ising created the Ising model which is essentially a non-learning RNN architecture consisting
Deep_learning
Polish-American Mathematician
introduced the spherical model of a ferromagnet, a variant of the Ising model, and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial
Mark_Kac
Theory of continuous phase transitions
the critical temperature. In a simple ferromagnetic system like the Ising model, the order parameter is characterized by the net magnetization m {\displaystyle
Landau_theory
Application of an external magnetic field to a ferromagnet
domains, often based on the Landau-Lifshitz-Gilbert equation. Toy models such as the Ising model can help explain qualitative and thermodynamic aspects of hysteresis
Magnetic_hysteresis
Numerical technique for solving quantum Hamiltonians
frequently employed to study lattice models, including the Hubbard model, Ising model, Heisenberg model, t-J model, and SYK model. After determining the eigenstates
Exact_diagonalization
dynamics. The Sznajd model implements a phenomenon called social validation and thus extends the Ising spin model. In simple words, the model states: Social
Sznajd_model
Complex structures in matter physics
systems had been studied even before. Early work includes a study of the Ising model on a triangular lattice with nearest-neighbor spins coupled antiferromagnetically
Geometrical_frustration
materials in the Ising model, enabling the study of phase transitions and critical phenomena. The Ising model, a mathematical model in statistical mechanics
Construction of an irreducible Markov chain in the Ising model
Construction_of_an_irreducible_Markov_chain_in_the_Ising_model
Regulation of enzyme activity
salt bridge between two domains). Ensemble models like the ensemble allosteric model and allosteric Ising model assume that each domain of the system can
Allosteric_regulation
model Information cascade Stock market crash Cascading failure Epidemic model Percolation_theory Self-organized criticality Ising model Voter model Complex
Global_cascades_model
Kurtosis of the order parameter in statistical physics
at a critical point. Measurements have been made for several systems: Ising model, square boundary with periodic b.c.: U = 0.6106901(5). (Note authors
Binder_parameter
Regular infinite tree structure used in statistical mechanics
other lattices, it can still provide useful insight. The Ising model is a mathematical model of ferromagnetism, in which the magnetic properties of a
Bethe_lattice
operator algebra formalism for the two-dimensional Ising model, a widely studied mathematical model of ferromagnetism in statistical physics. This development
History of quantum field theory
History_of_quantum_field_theory
Memoryless property of a stochastic process
for an interconnected network of items. An example of a model for such a field is the Ising model. A discrete-time stochastic process satisfying the Markov
Markov_property
algorithm), is an algorithm for Monte Carlo simulation of the Ising model and Potts model in which the unit to be flipped is not a single spin (as in the
Wolff_algorithm
The spherical model is a model of ferromagnetism similar to the Ising model, which was solved in 1952 by T. H. Berlin and M. Kac. It has the remarkable
Spherical_model
Mathematical model used to describe active matter
liquid have been modelled. A simpler theory, the Active Ising model, has been developed to facilitate the analysis of the Vicsek model. Vicsek, Tamás;
Vicsek_model
Family of solved 2D conformal field theories
{\displaystyle (p,q)=(4,3)} : critical Ising model, ( p , q ) = ( 5 , 4 ) {\displaystyle (p,q)=(5,4)} : tricritical Ising model, ( p , q ) = ( 6 , 5 ) {\displaystyle
Minimal_model_(physics)
Mathematics award
"For the proof of conformal invariance of percolation and the planar Ising model in statistical physics." Cédric Villani École Normale Supérieure de Lyon
Fields_Medal
Analog of the continuous Laplace operator
The discrete Laplace operator occurs in physics problems such as the Ising model and loop quantum gravity, as well as in the study of discrete dynamical
Discrete_Laplace_operator
Branch of physics
microscopic description of magnetism was by Wilhelm Lenz and Ernst Ising through the Ising model that described magnetic materials as consisting of a periodic
Condensed_matter_physics
German physicist
physicist, most notable for his invention of the Ising model (named after his student, Ernst Ising), and for his application of the Laplace–Runge–Lenz
Wilhelm_Lenz
Graph with sign-labeled edges
appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in Σ. They have
Signed_graph
Cellular automaton that can be run backwards
Additionally, many problems in physical modeling, such as the motion of particles in an ideal gas or the Ising model of alignment of magnetic charges, are
Reversible_cellular_automaton
Problem in graph theory
to minimizing the Hamiltonian of a spin glass model, most simply the Ising model. For the Ising model on a graph G and only nearest-neighbor interactions
Maximum_cut
Discrete model of computation
physics to study phenomena like fluid dynamics and phase transitions. The Ising model is a prototypical example, in which each cell can be in either of two
Cellular_automaton
American theoretical physicist (1925–2018)
since he first defined and investigated the stochastic dynamics of an Ising model in a paper published in 1963. He served on the National Advisory Board
Roy_J._Glauber
Quantum computing company
solve a particular NP-complete problem related to the two-dimensional Ising model in a magnetic field. D-Wave terms the device as a 16-qubit superconducting
D-Wave_Systems
Conformal field theory on a 2D spacetime
-state Potts model or critical random cluster model is a conformal field theory that generalizes and unifies the critical Ising model, Potts model, and percolation
Two-dimensional conformal field theory
Two-dimensional_conformal_field_theory
NP-hard with the (non-discretized) Euclidean metric. Three-dimensional Ising model Existential theory of the reals § Complete problems Karp's 21 NP-complete
List_of_NP-complete_problems
Swiss physicist (1911–1983)
ferromagnetic theory via the Ising model. The Kramers–Wannier duality yields the exact location of the critical point for the Ising model on the square lattice
Gregory_Wannier
_{i}{S_{i}}^{z}} , where S i z {\displaystyle {S_{i}}^{z}} is the Ising dipole moments. The J i j {\displaystyle {J_{ij}}} refers to the random
Dipole_glass
Rule forbidding the coherence of certain states
between symmetry breaking directions and conserved charges. In the 2D Ising model, at low temperatures, there are two distinct pure states, one with the
Superselection
Mathematical theory on behavior of connected clusters in a random graph
the Fortuin–Kasteleyn random cluster model, which has many connections with the Ising model and other Potts models. Bernoulli (bond) percolation on complete
Percolation_theory
Mathematical method to constrain and solve conformal field theories
field theory describing the critical point of the three-dimensional Ising model, it produced the most precise predictions for its critical exponents
Conformal_bootstrap
Mathematical function common in physics
"Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature". Phys. Rev. B. 37 (7): 3716–3719. Bibcode:1988PhRvB
Stretched exponential function
Stretched_exponential_function
Cellular automaton with probabilistic rules
disease epidemics, or the simulation of ferromagnetism in physics (see Ising model). As a mathematical object, a stochastic cellular automaton is a discrete-time
Stochastic_cellular_automaton
Physics of many interacting particles
found for a few toy models. Some examples include the Bethe ansatz, square-lattice Ising model in zero field, hard hexagon model. Although some problems
Statistical_mechanics
ISING MODEL
ISING MODEL
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Rising
Girl/Female
Tamil
Iron, Rising
Boy/Male
Indian, Punjabi, Sikh
Rising
Girl/Female
Hindu, Indian
Rising
Boy/Male
Tamil
Rising, Shining
Girl/Female
Bengali, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Rising
Boy/Male
Tamil
Rising
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Hindu, Indian, Tamil
Rising
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Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Rising
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Rising
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Rising, Shining
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Hindu, Indian
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Australian, French, German, Latin
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Sing
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Rising.
Boy/Male
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Uday Tej | உதய தேஜÂ
Rising Sun
Uday Tej | உதய தேஜÂ
Girl/Female
Tamil
Rising Sun
Boy/Male
Tamil
Udayasooriyan | உதயஸூரியாà®Â
Rising Sun
ISING MODEL
ISING MODEL
Boy/Male
Muslim
The prophet Yusuf as brothers name
Boy/Male
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Pen
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Gujarati, Hindu, Indian
Bright; Glowing; Lustrous
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Young.
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One who has the mace as his weapon
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American, Arabic, Australian, Muslim
Elevated; Lofty
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Punyodaya | பà¯à®¨à¯à®¯à¯‹à®¤à®¯à®¾
Provider of immortality
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Australian, Japanese
Child of Sakura
Boy/Male
Tamil
Victorious' href='Boy-Names-for-Meaning-Victorious.aspx'>Victorious, Victor
Girl/Female
Hindu
Devotion, Firmness
ISING MODEL
ISING MODEL
ISING MODEL
ISING MODEL
ISING MODEL
a.
Increasing in wealth, power, or distinction; as, a rising state; a rising character.
a.
Attaining a higher place; taking, or moving in, an upward direction; appearing above the horizon; ascending; as, the rising moon.
n.
The act of rising; appearance above the horizon; rising.
n.
Rising.
prep.
More than; exceeding; upwards of; as, a horse rising six years of age.
p. pr. & vb. n.
of Use
a.
Rising again.
a.
Growing; advancing to adult years and to the state of active life; as, the rising generation.
n.
That which rises; a tumor; a boil.
a.
Rising; ascending.
n.
Act of rising.
n.
The act of one who, or that which, rises (in any sense).
n.
The kob.
a.
Rising higher; ascending.
p. pr. & vb. n.
of Rise
n. sing. & pl.
A native or natives of Madagascar; also (sing.), the language.
a.
Rising above; surpassing.
v. t.
To influence by singing; to lull by singing; as, to sing a child to sleep.
n. sing. & pl.
A native or the natives of Burmah. Also (sing.), the language of the Burmans.
a.
Using; accustomed.