Higher orders of the high-temperature expansion for the Ising model in three dimensions

TL;DR

This paper introduces an advanced algorithm to generate high-temperature series expansions for the 3D Ising model, enabling precise determination of critical points and exponents.

Contribution

It presents a novel finite lattice method algorithm that extends the high-temperature series to higher orders for the 3D Ising model.

Findings

Precise critical point value determined

Critical exponents accurately estimated

Series extended to higher orders than previous studies

Abstract

The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic susceptibility and to $\beta^{29}$ for the second moment correlation length. The series are analyzed to give the precise value of the critical point and the critical exponents of the model.