Density of the Fisher zeros for the three-state and four-state Potts models

The numbers of states up to L=12 for the three-state Potts model and up to L=10 for the four-state Potts model on LxL square lattice with self-dual boundary condition are enumerated using the microcanonical transfer matrix exploiting the permutation symmetry of the model. From these numbers of states, the densities of the Fisher zeros g(theta) of the partition function in the complex u=(1+(Q-1) e(-betaJ) )/square root[Q] plane are determined for the zeros on the unit circle u(0) = e(itheta). For small theta the density of zeros obeys the finite-size scaling, allowing us to estimate the order parameter and the thermal exponent.