Gibbs measures of an Ising model with competing interactions on the triangular chandelier-lattice

TL;DR

This paper analyzes the Gibbs measures of an Ising model with competing interactions on a triangular chandelier-lattice, establishing conditions for phase transitions and providing explicit formulas for Gibbs measures with memory.

Contribution

It introduces explicit formulas for Gibbs measures with memory length 2 and rigorously characterizes phase transitions on the TCL, addressing the dichotomy in Hamiltonian solutions.

Findings

Phase transitions occur only for specific coupling constants.

Explicit formulas for Gibbs measures with memory length 2 are derived.

Numerical examples illustrate theoretical results.

Abstract

In this paper, we consider an Ising model with three competing interactions on a triangular chandelier-lattice (TCL). We describe the existence, uniqueness, and non-uniqueness of translation-invariant Gibbs measures associated with the Ising model. We obtain an explicit formula for Gibbs measures with a memory of length 2 satisfying consistency conditions. It is rigorously proved that the model exhibits phase transitions only for given values of the coupling constants. As a consequence of our approach, the dichotomy between alternative solutions of Hamiltonian models on TCLs is solved. Finally, two numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.