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

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.