scholarly journals Analytical expressions for a finite-size 2D Ising model

2017 ◽  
Vol 26 (3) ◽  
pp. 165-171 ◽  
Author(s):  
I. M. Karandashev ◽  
B. V. Kryzhanovsky ◽  
M. Yu. Malsagov
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Analytical Expressions

scholarly journals Investigation of Finite-Size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 585 ◽  
Author(s):  
Boris Kryzhanovsky ◽  
Magomed Malsagov ◽  
Iakov Karandashev
Keyword(s):  
Ising Model ◽  
Ground State ◽  
Multiplicative Noise ◽  
Finite Size ◽  
Gradual Change ◽  
Linear Dimensions ◽  
Spin Interactions ◽  
Glass Model ◽  
Analytical Expressions ◽  
Uncorrelated State

We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the transition reduces to a gradual change in the amplitude of the multiplicative noise (distributed uniformly with a mean equal to one) superimposed over the initial Ising matrix of interacting spins. Considering the noise, we obtain analytical expressions that are valid for lattices of finite sizes. We compare our results with the results of computer simulations performed for square N = L × L lattices with linear dimensions L = 50 ÷ 1000. We find experimentally the dependencies of the critical values (the critical temperature, the internal energy, entropy and the specific heat) as well as the dependencies of the energy of the ground state and its magnetization on the amplitude of the noise. We show that when the variance of the noise reaches one, there is a jump of the ground state from the fully correlated state to an uncorrelated state and its magnetization jumps from 1 to 0. In the same time, a phase transition that is present at a lower level of the noise disappears.

scholarly journals Finite-size behavior of the critical Ising model on a rectangle with free boundaries

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Xintian Wu ◽  
Nickolay Izmailian ◽  
Wenan Guo
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Free Boundaries

scholarly journals Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Finite Lattices ◽  
Antiferromagnetic Ising Model ◽  
Boundary Fields

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

scholarly journals Finite size effects for the Ising Model coupled to 2-D random surfaces

1996 ◽  
Vol 368 (1-2) ◽  
pp. 55-63 ◽  
Author(s):  
N.D. Hari Dass ◽  
B.E. Hanlon ◽  
T. Yukawa
Keyword(s):  
Ising Model ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
Random Surfaces

Thermodynamic Bethe Ansatz

2020 ◽  
pp. 791-835
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Bethe Ansatz ◽  
Free Field ◽  
Integrable Model ◽  
Finite Size ◽  
Casimir Energy ◽  
Thermodynamic Bethe Ansatz ◽  
Channel Quantization ◽  
Bulk Energy ◽  
Energy And Momentum

The Thermodynamic Bethe Ansatz (TBA) allows us to study finite size and finite temperature effects of an integrable model. This chapter investigates the integral equations that determine the free energy and gives their physical interpretation. It discusses Casimir energy, Bethe relativistic wave function, the derivation of thermodynamics, the meaning of pseudo-energy (dressed energy and momentum), infrared and ultraviolet limits, the coefficient of bulk energy, the general form of the TBA equations, the thermodynamics of the free field theories, L-channel quantization and the LeClair–Mussardo formula. It also covers the application of the Yang–Lee S-matrix, the magnetic field Ising model, and the tricritical Ising model.

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