Anisotropic simple-cubic Ising lattice: extended phenomenological renormalization-group treatment

TL;DR

This paper employs transfer-matrix extended phenomenological renormalization-group methods to accurately estimate the critical temperature of an anisotropic simple-cubic Ising lattice, confirming universality of critical exponents and independence of certain amplitude ratios from anisotropy.

Contribution

It provides improved critical temperature estimates for the anisotropic simple-cubic Ising model and confirms the universality of critical exponents and amplitude ratios across anisotropy levels.

Findings

Critical temperature estimates are refined.

Universality of critical exponents $y_t$ and $y_h$ is confirmed.

Finite-size scaling amplitude ratios are independent of anisotropy.

Abstract

Using transfer-matrix extended phenomenological renormalization-group methods [M.A.Yurishchev, Nucl. Phys. B (Proc. Suppl.) 83-84, 727 (2000); hep-lat/9908019; J. Exp. Theor. Phys. 91, 332 (2000); cond-mat/0108002] the improved estimates for the critical temperature of spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ 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 $A_{\chi^{(4)}}A_\kappa/A_\chi^2$, $A_{\kappa^{''}}/A_\chi$, and $A_{\kappa^{(4)}}/A_{\chi^{(4)}}$ are independent of the lattice anisotropy parameter $\Delta=J'/J$.