Monte Carlo studies of the Ising square lattice with competing interactions

TL;DR

This study uses advanced Monte Carlo methods to explore the phase diagram of the 2D Ising model with competing interactions, revealing a critical point with degenerate ground states and a first-order transition.

Contribution

It provides new insights into the phase boundaries and transition types of the antiferromagnetic 2D Ising model with next-nearest neighbor interactions.

Findings

First-order transition for small J2 > J1/2

Transition temperature drops to zero at the critical point

Phase diagram features a highly degenerate ground state at J2 = J1/2

Abstract

We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions $J_1$ on nearest neighbour and $J_2$ on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at $J_2 = J_1/2$ where the groundstate is highly degenerate. To analyse the phase boundaries we look at the specific heat and the energy distribution for various ratios of $J_2/J_1$. We find a first order transition for small $J_2 > J_1/2$ and the transition temperature suppressed to $T_C=0$ at the critical point.