TY - JOUR
T1 - Obtaining critical point and shift exponent for the anisotropic two-layer Ising and Potts models
T2 - Cellular automata approach
AU - Asgari, Yazdan
AU - Ghaemi, Mehrdad
PY - 2008/3/15
Y1 - 2008/3/15
N2 - Using probabilistic cellular automata with the Glauber algorithm, we have precisely calculated the critical points for the anisotropic two-layer Ising and Potts models (Kx ≠ Ky ≠ Kz) of the square lattice, where Kx and Ky are the nearest-neighbor interactions within each layer in the x and y directions, respectively and Kz is the inter-layer coupling. A general equation is obtained as a function of the inter- and intra-layer interactions (ξ, σ) for both the two-layer Ising and Potts models, separately, where ξ = Kz / Kx and σ = Ky / Kx. Furthermore, the shift exponent for the two-layer Ising and Potts models is calculated. It was demonstrated that in the case of σ = 1 for the two-layer Ising model, the value of φ{symbol} = 1.756 (± 0.0078) supports the scaling theories' prediction that φ{symbol} = γ. However, for the unequal intra-layer couplings for the two-layer Ising model and also in the case of both equal and unequal intra-layer interactions for the two-layer Potts model, our results are different from those obtained from the scaling theories. Finally, an equation is obtained for the shift exponent as a function of intra-layer couplings (σ) for the two-layer Ising and Potts models.
AB - Using probabilistic cellular automata with the Glauber algorithm, we have precisely calculated the critical points for the anisotropic two-layer Ising and Potts models (Kx ≠ Ky ≠ Kz) of the square lattice, where Kx and Ky are the nearest-neighbor interactions within each layer in the x and y directions, respectively and Kz is the inter-layer coupling. A general equation is obtained as a function of the inter- and intra-layer interactions (ξ, σ) for both the two-layer Ising and Potts models, separately, where ξ = Kz / Kx and σ = Ky / Kx. Furthermore, the shift exponent for the two-layer Ising and Potts models is calculated. It was demonstrated that in the case of σ = 1 for the two-layer Ising model, the value of φ{symbol} = 1.756 (± 0.0078) supports the scaling theories' prediction that φ{symbol} = γ. However, for the unequal intra-layer couplings for the two-layer Ising model and also in the case of both equal and unequal intra-layer interactions for the two-layer Potts model, our results are different from those obtained from the scaling theories. Finally, an equation is obtained for the shift exponent as a function of intra-layer couplings (σ) for the two-layer Ising and Potts models.
KW - Cellular automata
KW - Critical point
KW - Ising model
KW - Potts model
KW - Shift exponent
UR - http://www.scopus.com/inward/record.url?scp=38349039325&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2007.11.025
DO - 10.1016/j.physa.2007.11.025
M3 - Article
AN - SCOPUS:38349039325
SN - 0378-4371
VL - 387
SP - 1937
EP - 1946
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 8-9
ER -