Journal of Experimental and Theoretical Physics

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

M. A. Yurishchev

Published Jun 1, 2004• 6 citations

Abstract

The Ising model is considered on a simple cubic lattice, with a coupling constant J along one axis and coupling constants J’ along the remaining two axes. The transfer-matrix technique and an extended phenomenological renormalization group theory [18, 19] are applied to obtain two-sided bounds on the critical temperature for the model with J′/J ≤1. The bounds monotonically converge with decreasing J′/J and provide improved estimates for the phase-transition temperature in anisotropic three-dimensional Ising model, as compared with those available from the literature.

DOI: 10.1134/1.1777631

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Journal of Experimental and Theoretical Physics

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

M. A. Yurishchev

Published Jun 1, 2004• 6 citations

Publisher

Abstract

DOI: 10.1134/1.1777631

Related papers

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M. A. Yurishchev

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{\vec J}=(J',J',J)

are obtained. Universality of both fundamental critical exponents

y_t

and

y_h

is confirmed. We show also that the critical finite-size scaling amplitude ratios

A_{χ^{(4)}}A_κ/A_χ^2

A_{κ^{''}}/A_χ

, and

A_{κ^{(4)}}/A_{χ^{(4)}}

are independent of the lattice anisotropy parameter

Δ=J'/J

\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).