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

Meik Hellmund·Wolfhard Janke
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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 $D\leq3$, order 19 for $D\leq 5$ 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 $γ$ 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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Meik Hellmund, Wolfhard Janke. 2006-08-25. High-temperature series expansions for the $q$-state Potts model on a hypercubic lattice and critical properties of percolation. https://doi.org/10.1103/physreve.74.051113

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