arXiv:cond-mat/0203609 · Journal of Physics Condensed Matter

The critical temperature of a fully anisotropic three-dimensional Ising model

M. A. Yurishchev

Published Oct 25, 1993• 4 citations

Abstract

The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite-size scaling for L*L* infinity clusters (L=2 and 3). The results obtained are compared with available calculations. An exact analytical solution is found for the 2*2* infinity Ising chain with fully anisotropic interactions (arbitrary J x , J y and J z ).

DOI: 10.1088/0953-8984/5/43/019

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arXiv:cond-mat/0203609 · Journal of Physics Condensed Matter

The critical temperature of a fully anisotropic three-dimensional Ising model

M. A. Yurishchev

Published Oct 25, 1993• 4 citations

arXiv HTML PDF

Abstract

The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite-size scaling for LL infinity clusters (L=2 and 3). The results obtained are compared with available calculations. An exact analytical solution is found for the 22 infinity Ising chain with fully anisotropic interactions (arbitrary J x , J y and J z ).

DOI: 10.1088/0953-8984/5/43/019

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\mathop J\limits^ \to = (J',J',J)

. The universality of both fundamental critical exponents y t and y h is confirmed. It is shown that the critical finite-size scaling amplitude ratios

U = A_{\chi ^{(4)} } A_\kappa /A_\chi ^2 ,Y_1 = A_{\kappa ''} /A_\chi

, and

Y_2 = A_{\kappa ^{(4)} } /A_{\chi ^{(4)} }

are independent of the lattice anisotropy parameter Δ=J′/J. For the Y 2 invariant of the three-dimensional Ising universality class, we give the first quantitative estimate Y 2≈2.013 (shape L×L×∞, periodic boundary conditions in both transverse directions).