First order phase transition of the q-state Potts model in two dimensions

We have calculated the large-$q$ series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the $q$-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of $10^2 - 10^4$ than the Monte Carlo simulations. From the large-$q$ series of the eigenvalues of the transfer matrix, we also find that the excited states form a continuum spectrum and there is no particle state at the first order phase transition point.