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 $D^{-9}$.

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• Critical behavior of 3D Z(N) lattice gauge theories at zero temperature
• Linked-cluster expansions for quantum magnets on the hypercubic lattice
• Quantum criticality in the 2d quasiperiodic Potts model
• The SU(3) spin model with chemical potential by series expansion techniques
• Clusters' size-degree distribution for bond percolation