Kagome Approximation for 3He on Husimi Lattice with Two- and Three-Site Exchange Interactions

TL;DR

This paper studies an Ising approximation of the Heisenberg model with exchange interactions on a Husimi lattice, revealing magnetization behaviors, phase transitions, and Yang-Lee zeros relevant to 3He on graphite surfaces.

Contribution

It introduces an exact recursion relation approach for the model and analyzes its magnetic and phase properties, including magnetization plateaus and Yang-Lee zeros.

Findings

Magnetization varies from ferromagnetic to antiferromagnetic depending on parameters.

A 1/3 magnetization plateau is observed in the antiferromagnetic case.

Yang-Lee zeros lie on arcs of the circle with radius 1.

Abstract

The Ising approximation of the Heisenberg model in a strong magnetic field, with two-, and three-spin exchange interactions are studied on a Husimi lattice. This model can be considered as an approximation of the third layer of 3He absorbed on the surface of graphite (kagome lattice). Using dynamic approach we have found exact recursion relation for the partition function. For different values of exchange parameters and temperature the diagrams of magnetization are plotted and showed that magnetization properties of the model vary from ferromagnetic to antiferromagnetic depending from the value of model parameters. For antiferromagnetic case magnetization plateau at 1/3 of saturation field is obtained. Lyapunov exponent for recursion relation are considered and showed absents of bifurcation points in thermodynamic limit. The Yang-Lee zeros are analyzed in terms of neutral fixed points and showed that Yang-Lee zeros of the model are located on the arcs of the circle with the radius R=1.