Zero-Temperature Phase Transitions of Antiferromagnetic Ising Model of General Spin on a Triangular Lattice

TL;DR

This paper investigates the ground-state phase transitions of the antiferromagnetic Ising model with general spin on a triangular lattice, using an interface mapping and Monte Carlo simulations to identify multiple phases and critical points.

Contribution

It introduces an interface model representation for the ground states of the spin-S Ising model, enabling precise calculation of critical exponents and phase boundaries.

Findings

Identification of three distinct phases in the model.

Detection of a Kosterlitz-Thouless phase transition between phases.

Observation of a locking phase transition at specific spin values.

Abstract

We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a triangular lattice to an interface model whose entropic fluctuations are proposed to be described by an effective Gaussian free energy, which enables us to calculate the critical exponents of various operators in terms of the stiffness constant of the interface. Monte Carlo simulations for the ground-state ensemble utilizing this interfacial representation are performed to study both the dynamical and the static properties of the model. This method yields more accurate numerical results for the critical exponents. By varying the spin magnitude in the model, we find that the model exhibits three phases with a Kosterlitz-Thouless phase transition at 3/2<S_{KT}<2 and a locking phase transition at 5/2 < S_L \leq 3. The phase diagram at finite temperatures is also discussed.