Low-Temperature Series for the Square Lattice Potts Model by the Improved Finite-Lattice Method

TL;DR

This paper computes low-temperature series for the square lattice Potts model's thermodynamic quantities using an improved finite lattice method, extending to high orders and comparing with other analytical and numerical approaches.

Contribution

It introduces an improved finite lattice method to generate high-order low-temperature series for the Potts model, enhancing accuracy and comparison with existing methods.

Findings

Series obtained up to order z^{41} for Q=5-50.

Padé analysis aligns well with large-Q expansion and Monte Carlo results.

Demonstrates the effectiveness of the improved algorithm for high-order series.

Abstract

The low-temperature series are calculated for the free energy, magnetization and susceptibility in the Q-state Potts model on the square lattice, using the improved algorithm of the finite lattice method. The series are obtained to the order of $z^{41}$ for each of Q=5-50, and the result of their Pad\'e type analysis is compared with those of the large-Q expansion and the Monte Carlo simulations.