High-temperature series expansions for the $q$-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 ${\mathbb{Z}}^D$ for arbitrary values of $q$. The series are up to order 20 for dimension $D\le 3$, order 19 for $D\le 5$ and up to order 17 for arbitrary $D$. Using the $q\to 1$ limit of these series, we estimate the percolation threshold $p_c$ 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 $D^{-9}$.

2 references added

References in corpus (1)

• The Universal Amplitude Ratio ${\Gamma }^{-}/{\Gamma }^{+}$ for Two-Dimensional Percolation

Cited by in corpus (3)

• Phase Transition Properties of 3D Potts Models
• Percolation of Vortices in the 3D Abelian Lattice Higgs Model
• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase