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. 
Tahmasb Mardani, Behrouz Mirza, Mehrdad Ghaemi