Phase transition in magnetically coupled spins on a ring (SOR) model

TL;DR

This study introduces a new XY spin model on concentric rings, demonstrating a finite temperature phase transition without vortex formation, using Monte Carlo simulations to analyze its critical behavior.

Contribution

The paper presents a novel ring-based XY model with continuous spins and investigates its phase transition properties through Monte Carlo simulations, revealing unique stable states and transition characteristics.

Findings

Finite temperature order-disorder phase transition observed.

No vortex formation detected in the model.

Two stable states identified at zero temperature.

Abstract

We have considered a new type of 'XY' model where spins are placed on concentric ring with constant spin density in every ring. The spin executes continuous rotation under a modified Shore-Zwanzig Hamiltonian (J. Chem. Phys. 63, 5445 (1975)). We have performed Monte Carlo simulation using Glauber acceptance criteria. Computations of Binder's cumulant, specific heat and magnetic susceptibility all show presence of a finite temperature order-disorder phase transition in this spin system. The system size dependence of Binder's cumulant suggests the existence of a phase transition with a transition temperature of T* = 1.2. However, we have found no signature of the occurrence of vortex in our SOR model. The absence of hysteresis rules out the possibility of first order phase transition. We have found two "stable" states for T* = 0 phase. The perfectly ordered true ground state is obtained by gradual cooling of the system, while the other is obtained by starting the simulation with a random configuration at T* = 0. This second state has higher energy than the perfectly aligned ground state.