Correlation Functions of the Ising Model with Multisite Interaction on the Husimi Lattice

TL;DR

This paper derives analytical correlation functions for a generalized Ising model with multisite interactions on the Husimi lattice, revealing connections to vertex models and Bethe lattice models through specific transformations.

Contribution

It provides explicit formulas for correlation functions in a multisite-interaction Ising model on the Husimi lattice and links these to Bethe lattice models via analytical transformations.

Findings

Correlation functions derived for the model at different q values.

Model reduces to known vertex and Bethe lattice models under certain conditions.

Analytical expressions facilitate understanding of phase behavior and correlations.

Abstract

We consider a general spin-1/2 Ising model with multisite interaction on the Husimi lattice with the coordination number q and derive an analytical expression of correlation functions for stable fixed points of the corresponding recurrence relation. We show that for q=2 our model transforms to the two-state vertex model on the Bethe lattice with q=3 and for the case q=3, with only nearest neighbour interactions, we transform our model to the corresponding model on the Bethe lattice with q=3, using the Yang-Baxter equations.