the critical exponents using the operator dimensions values from the following table: In d=2, the two-dimensional critical Ising model's critical exponents...
10 KB (880 words) - 13:43, 9 June 2025
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical...
88 KB (13,240 words) - 00:12, 11 June 2025
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...
15 KB (3,287 words) - 13:34, 30 August 2024
The Ising model is a prototypical model in statistical physics. The model consists of discrete variables that represent magnetic dipole moments of atomic...
35 KB (6,317 words) - 01:09, 11 June 2025
Conformal field theory (section Critical Ising model)
all spins. The two-dimensional critical Ising model includes the M ( 4 , 3 ) {\displaystyle {\mathcal {M}}(4,3)} Virasoro minimal model, which can be solved...
42 KB (7,031 words) - 08:27, 18 May 2025
divergence in the specific heat. Indeed, like the one-dimensional Ising model, the one-dimensional XY model has no phase transitions at finite temperature....
31 KB (4,861 words) - 22:58, 14 January 2025
minimal model with c = c 4 , 3 = 1 2 {\displaystyle c=c_{4,3}={\tfrac {1}{2}}} describes spin and energy correlators of the two-dimensional critical Ising model...
33 KB (5,674 words) - 01:40, 21 January 2025
Ising model, which has a diagonal partition function in terms of Virasoro characters. It is possible to obtain the critical three-state Potts model from...
9 KB (1,747 words) - 18:17, 27 April 2024
shall use the Ising model as a pedagogical example. Consider a 2 D {\displaystyle 2D} square array of classical spins which may only take two positions:...
12 KB (1,578 words) - 07:06, 22 April 2025
high dimensions or when exact solutions are known such as the two-dimensional Ising model. The theoretical treatment in generic dimensions requires the...
19 KB (2,211 words) - 11:09, 15 November 2024
Social physics (section Ising model and voter dynamics)
Ising model. In the social physics model, each spin denotes an opinion, e.g. yes or no, and each space represents a "voter".[citation needed] If two adjacent...
17 KB (1,994 words) - 12:51, 6 June 2025
the two-dimensional square lattice Ising model is a simple lattice model of interacting magnetic spins, an example of the class of Ising models. The...
15 KB (2,664 words) - 18:46, 10 June 2025
Magnetic 2D materials (category Two-dimensional nanomaterials)
with n = 1 {\displaystyle n=1} is described by the 2D Ising model. Onsager's solution to the model demonstrates that T C > 0 {\displaystyle T_{C}>0} , thus...
17 KB (2,124 words) - 02:04, 25 May 2025
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...
7 KB (1,193 words) - 03:27, 20 January 2025
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...
13 KB (1,984 words) - 22:47, 13 May 2025
by Oded Schramm. He also established conformality for the two-dimensional critical Ising model. Smirnov was awarded the Saint Petersburg Mathematical Society...
7 KB (551 words) - 11:08, 26 October 2024
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...
16 KB (2,733 words) - 03:57, 2 June 2025
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...
23 KB (3,645 words) - 09:43, 26 February 2025
{\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...
5 KB (1,047 words) - 05:09, 1 May 2024
materials in the Ising model, enabling the study of phase transitions and critical phenomena. The Ising model, a mathematical model in statistical mechanics...
7 KB (1,141 words) - 15:31, 30 August 2024
Percolation theory (section Different models)
modelled mathematically as a three-dimensional network of n × n × n vertices, usually called "sites", in which the edge or "bonds" between each two neighbors...
26 KB (3,133 words) - 05:14, 12 April 2025
of critical properties of lattice models, one can recover the results of dimensional analysis in the appropriate scaling limit; e.g., dimensional analysis...
96 KB (11,968 words) - 12:10, 15 June 2025
Glauber dynamics (category Spin models)
simulate the Ising model (a model of magnetism) on a computer. The algorithm is named after Roy J. Glauber. The Ising model is an abstract model for the magnetic...
6 KB (889 words) - 12:27, 13 June 2025
Kramers–Wannier duality (category Exactly solvable models)
relates the free 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...
12 KB (1,891 words) - 06:48, 31 May 2025
described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase...
35 KB (4,376 words) - 13:35, 25 May 2025
Phase transition (category Critical phenomena)
of the heat capacity at the transition temperature, and the two-dimensional Ising model has a logarithmic divergence. However, these systems are limiting...
54 KB (6,649 words) - 18:05, 25 May 2025
theory describing the critical points of the two-dimensional Ising model there is an operator σ {\displaystyle \sigma } whose dimension is 1/8. Operator multiplication...
7 KB (959 words) - 13:32, 9 June 2025
J. Ruiz-Lorenzo (1999). "Scaling corrections: site percolation and Ising model in three dimensions". Journal of Physics A. 32 (1): 1–13. arXiv:cond-mat/9805125...
69 KB (6,563 words) - 14:07, 26 May 2025
Scale invariance (category Critical phenomena)
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...
32 KB (4,486 words) - 01:39, 2 June 2025
Curie temperature (category Critical phenomena)
structure occurs at the Curie temperature. The Ising model is mathematically based and can analyse the critical points of phase transitions in ferromagnetic...
48 KB (4,937 words) - 15:13, 4 June 2025