High-temperature series expansions for theq-state Potts model on a hypercubic lattice and critical properties of percolation

Abstract

We present results for the high-temperature series expansions of the susceptibility and free energy of the q-state Potts model on a D-dimensional hypercubic lattice ZD for arbitrary values of q. The series are up to order 20 for dimension D<or=3, order 19 for D<or=5, and up to order 17 for arbitrary D. Using the q-->1 limit of these series, we estimate the percolation threshold pc and critical exponent gamma for bond percolation in different dimensions. We also extend the 1/D expansion of the critical coupling for arbitrary values of q up to order D-9.