The dual model for an Ising model with nearest and next-nearest neighbors

TL;DR

This paper constructs a dual model for the Ising model with nearest and next-nearest neighbors, revealing how four-spin interactions influence the critical temperature within a finite range.

Contribution

It introduces a dual model with two- and four-spin interactions for the NNNI Ising model and analyzes the impact on critical temperature using free fermion approximation.

Findings

Four-spin interactions limit the increase in critical temperature.

The dual model contains both two- and four-spin interactions.

Critical temperature changes are bounded within a finite range.

Abstract

We construct and analyse a dual model to the Ising model with the nearest and next-nearest neighbors on the rectangular lattice (NNNI model). The Hamiltonian of the dual model turns out to contain two- and four-spin interactions. The free fermion approximation suggests that an increase in the critical temperature of the dual model caused by the four-spin interactions is limited to a finite range.