Extrapolation procedure for low-temperature series for the square lattice spin-1 Ising model

TL;DR

This paper introduces a new extrapolation method combined with finite-lattice series expansions to extend the low-temperature series for key thermodynamic quantities of the spin-1 Ising model on a square lattice, achieving higher-order terms.

Contribution

A novel extrapolation procedure is developed and applied to extend low-temperature series for the spin-1 Ising model, reaching higher-order terms than previously possible.

Findings

Extended series to order 99 in the variable u

Calculated an additional 13-14 terms using the new method

Enhanced accuracy of low-temperature thermodynamic predictions

Abstract

The finite-lattice method of series expansions has been combined with a new extrapolation procedure to extend the low-temperature series for the specific heat, spontaneous magnetisation and susceptibility of the spin-1 Ising model on the square lattice. The extended series were derived by directly calculating the series to order 99 (in the variable $u=\exp[-J/k_B T])$ and using the new extrapolation procedure to calculate an additional 13--14 terms.