Calculation of the shift exponent for the two layer three state Potts model using the transfer matrix method

TL;DR

This paper develops a transfer matrix-based finite-size scaling method to compute the critical temperature and shift exponent of two-layer three-state Potts models, confirming some scaling predictions and revealing deviations in asymmetric cases.

Contribution

It introduces a transfer matrix approach for calculating critical exponents in two-layer Potts models, providing new insights into the shift exponent behavior.

Findings

Confirmed $ ext{phi} = ext{gamma}$ for symmetric interactions.

Found $ ext{phi} = 0.5$ for asymmetric interactions.

Deviates from mean-field predictions in asymmetric cases.

Abstract

A finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature and critical exponent of the symmetric and the asymmetric two-layer three-state Potts Models. For similar intralayer interactions our calculation of the shift exponent $\phi $ confirm some scaling arguments which predict $\phi = \gamma$, where $\gamma$ is the susceptibility exponent. For unequal intralayer interactions we have obtained $\phi = 0.5 $ which differs from the prediction $\phi = {\gamma / 2} $ of a generalized mean-field theory.