Obtaining critical point and shift exponent for the anisotropic two-layer Ising and Potts models: Cellular automata approach

Asgari, Yazdan; Ghaemi, Mehrdad

doi:10.1016/j.physa.2007.11.025

Cited by 10 publications

(6 citation statements)

References 34 publications

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“…For ferromagnetic model on multilayered lattice, the phase transition behavior belongs to the same universality class as that in the corresponding single-layer lattice [27][28][29] , according to the hypothesis of universality. However, for antiferromagnetic model, due to the lattice structure dependence nature of the model, the number of layers may lead to substantially different behavior of phase transition from that in the corresponding single-layer lattice.…”

Section: Conclusion and Discussionmentioning

confidence: 96%

Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in a three-state Potts antiferromagnetic thin film

2014

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Using Monte Carlo simulations and finite-size scaling, we study three-state Potts antiferromagnet on layered square lattice with two and four layers Lz = 2 and 4. As temperature decreases, the system develops quasi-long-range order via a Berezinskii-Kosterlitz-Thouless transition at finite temperature Tc1. For Lz = 4, as temperature is further lowered, a long-range order breaking the Z6 symmetry develops at a second transition at Tc2 < Tc1. The transition at Tc2 is also BerezinskiiKosterlitz-Thouless-like, but has magnetic critical exponent η = 1/9 instead of the conventional value η = 1/4. The emergent U (1) symmetry is clearly demonstrated in the quasi-long-range ordered region Tc2 ≤ T ≤ Tc1.

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Section: Conclusion and Discussionmentioning

confidence: 96%

Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in a three-state Potts antiferromagnetic thin film

2014

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“…We have considered similar simulation procedure to find the optimal t max with lattice size 64 × 64 for different t max i.e., 2 13 , 2 14 , 2 15 , 2 16 , 2 17 and 2 18 . One of the simulation result given in figure 2 shows that t max = 2 17 is the best.…”

Section: Simulation To Find Maximum Iterationmentioning

confidence: 99%

“…Although the Q2R and Creutz CA models are deterministic and fast, it has been demonstrated that the probabilistic model of the CA like Metropolis algorithm is more realistic for description of the Ising model even though the random number generation makes it slower. Probabilistic CA model under periodic bc has been studied in the context of an anisotropic-layer (nearest-neighbor interactions within each layer are different) Ising and Potts models to find the critical point and shift exponent between two-layers [18]. However, Ising model using two dimensional CA under different bcs other than period has not yet been studied.…”

Section: Introductionmentioning

confidence: 99%

A comparative study of 2d Ising model at different boundary conditions using Cellular Automata

Mohammed

Mahapatra

2018

Int. J. Mod. Phys. C

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Using Cellular Automata, we simulate spin systems corresponding to 2d Ising model with various kinds of boundary conditions (bcs). The appearance of spontaneous magnetization in the absence of magnetic field is studied with a 64 × 64 square lattice with five different bcs, i.e., periodic, adiabatic, reflexive, fixed (+1 or −1) bcs with three initial conditions (all spins up, all spins down and random orientation of spins). In the context of 2d Ising model, we have calculated the magnetisation, energy, specific heat, susceptibility and entropy with each of the bcs and observed that the phase transition occurs around T c = 2.269 as obtained by Onsager. We compare the behaviour of magnetisation vs temperature for different types of bcs by calculating the number of points close to the line of zero magnetisation after T > T c at various lattice sizes. We observe that the periodic, adiabatic and reflexive bcs give closer approximation to the value of T c than fixed +1 and fixed -1 bcs with all three initial conditions for lattice size less than 70 × 70. However, for lattice size between 70 × 70 and 100 × 100, fixed +1 bc and fixed -1 bc give closer approximation to the T c with initial conditions all spin down configuration and all spin up configuration respectively.

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“…The previous approach could easily be used for calculation critical point of anisotropic twolayer Ising and Potts models which have different interlayer coupling coefficients ( &Ghaemi, 2006 andGhaemi, 2008 Table 1. The results are compared with other numerical methods and it is shown that they are in good agreement.…”

Section: Constructing the Critical Curve For Anisotropic Two-layer Momentioning

confidence: 99%

Cellular Automata Simulation of Two-Layer Ising and Potts Models

Ghaemi¹

2011

Cellular Automata - Simplicity Behind Complexity

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Obtaining critical point and shift exponent for the anisotropic two-layer Ising and Potts models: Cellular automata approach

Cited by 10 publications

References 34 publications

Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in a three-state Potts antiferromagnetic thin film

Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in a three-state Potts antiferromagnetic thin film

A comparative study of 2d Ising model at different boundary conditions using Cellular Automata

Cellular Automata Simulation of Two-Layer Ising and Potts Models

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