Phase diagram of the Ising square lattice with competing interactions

TL;DR

This study uses Monte Carlo simulations to map the phase diagram of the 2D Ising model with competing nearest and next-nearest neighbor interactions, revealing transition behaviors near critical points.

Contribution

It introduces computational methods to accurately determine transition temperatures near critical points and characterizes the nature of phase transitions in the model.

Findings

Transition temperatures close to the critical point are accurately calculated.

The phase transition is weakly first order for moderate $J_2 > 0.5 J_1$.

Finite temperature phase diagram of the model is mapped.

Abstract

We restudy the phase diagram of the 2D-Ising model with competing interactions $J_1$ on nearest neighbour and $J_2$ on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the critical point at $J_2 = 0.5 J_1$. Further on we investigate the character of the different phase boundaries and find that the transition is weakly first order for moderate $J_2 > 0.5 J_1$.