Low-temperature expansions for Potts models

High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model

We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order beta;{33} by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as beta_{c}=1.1200(1) , which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the multiplicative logarithmic correction is evaluated to be theta=0.054(10) , which is consistent with the renormalization group prediction of theta=1/16 .

Algorithm of the finite-lattice method for high-temperature expansion of the Ising model in three dimensions

We propose an algorithm of the finite-lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple-cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.