Series studies of the Potts model. II: Bulk series for the square lattice

TL;DR

This paper extends low-temperature series for the Potts model on a square lattice to high orders, providing data to analyze phase transition types and new numerical values for models with q>4.

Contribution

It applies the finite lattice method to generate high-order series expansions for the Potts model, enabling improved analysis of phase transitions and providing new numerical data for q>4.

Findings

Series extended to order z^{56} for q=2

Series extended to order z^{39} for q=4

New numerical values for q>4 Potts models

Abstract

The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $q$-state Potts model to order $z^{56}$ (i.e. $u^{28}$), $z^{47}$, $z^{43}$, $z^{39}$, $z^{39}$, $z^{39}$, $z^{35}$, $z^{31}$ and $z^{31}$ for $q = 2$, 3, 4, \dots 9 and 10 respectively. These series are used to test techniques designed to distinguish first-order transitions from continuous transitions. New numerical values are also obtained for the $q$-state Potts model with $q>4$.