Monte Carlo simulations of the classical two-dimensional discrete frustrated $\phi ^4$ model

TL;DR

This study uses Monte Carlo simulations to explore phase transitions and ground states in a two-dimensional frustrated $$ model, revealing complex behaviors including incommensurate phases and Kosterlitz-Thouless transitions.

Contribution

First Monte Carlo analysis of the 2D frustrated $$ model, identifying phase transitions and ground states for different frustration parameters.

Findings

Ground state is ferro-phase at d=-0.35

Incommensurate phase with period N=6 at d=-0.45

Two phase transitions with an incommensurate phase at d=-0.45

Abstract

The classical two-dimensional discrete frustrated $\phi ^4$ model is studied by Monte Carlo simulations. The correlation function is obtained for two values of a parameter $d$ that determines the frustration in the model. The ground state is a ferro-phase for $d=-0.35$ and a commensurate phase with period N=6 for $d=-0.45$. Mean field predicts that at higher temperature the system enters a para-phase via an incommensurate state, in both cases. Monte Carlo data for $d=-0.45$ show two phase transitions with a floating-incommensurate phase between them. The phase transition at higher temperature is of the Kosterlitz-Thouless type. Analysis of the data for $d=-0.35$ shows only a single phase transition between the floating-fluid phase and the ferro-phase within the numerical error.