Thermodynamics of Ising Spins on the Star Lattice

TL;DR

This paper analyzes the thermodynamics of Ising spins on a star lattice, relevant to new magnetic materials, using exact and simulation methods to reveal phase diagrams and ground states.

Contribution

It provides the first exact analytic solution for Ising spins on the star lattice and explores their thermodynamic properties and phase behavior.

Findings

Derived the partition function for the star lattice system.

Identified disordered spin liquid ground state with residual entropy.

Mapped phase diagrams showing transitions under varying interactions and fields.

Abstract

There is a new class of two-dimensional magnetic materials polymeric iron (III) acetate fabricated recently in which Fe ions form a star lattice. We study the thermodynamics of Ising spins on the star lattice with exact analytic method and Monte Carlo simulations. Mapping the star lattice to the honeycomb lattice, we obtain the partition function for the system with asymmetric interactions. The free energy, internal energy, specific heat, entropy and susceptibility are presented, which can be used to determine the sign of the interactions in the real materials. Moreover, we find the rich phase diagrams of the system as a function of interactions, temperature and external magnetic field. For frustrated interactions without external field, the ground state is disordered (spin liquid) with residual entropy 1.522 per unit cell. When a weak field is applied, the system enters a ferrimagnetic phase with residual entropy ln4 per unit cell.