Phase transitions of antiferromagnetic Ising spins on the zigzag surface of an asymmetrical Husimi lattice

TL;DR

This paper models antiferromagnetic Ising spins on a zigzag surface of an asymmetrical Husimi lattice to analyze phase transitions, revealing a first order transition and a secondary transition related to the Kauzmann paradox.

Contribution

It introduces a recursive lattice approach to study surface phase transitions in an asymmetrical 2D Ising model, providing exact calculations of thermodynamic properties.

Findings

Identified a first order order-disorder transition.

Detected a secondary transition in the supercooled state.

Analyzed thermodynamics on a zigzag surface of an asymmetrical lattice.

Abstract

An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice, which we have previously applied to study polymers near a surface. The model retains the advantages of simple formulation and exact calculation of the conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on the surface of this lattice to evaluate thermal properties such as free energy, energy density and entropy, from which we have successfully identified a first order order-disorder transition other than the spontaneous magnetization, and a secondary transition on the supercooled state indicated by the Kauzmann paradox.