Low temperature expansion for the 3-d Ising Model

TL;DR

This paper develops a recursive enumeration method to compute the weak coupling expansion of the 3D Ising model's energy and magnetization, effectively reducing finite volume effects through innovative boundary conditions.

Contribution

It introduces a novel recursive enumeration approach combined with generalized helical boundary conditions for precise weak coupling expansions in 3D Ising models.

Findings

Computed energy expansion up to 48 excited bonds

Calculated magnetization up to 40 excited bonds

Reduced finite volume effects with new boundary conditions

Abstract

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.