Qualitative aspects of the phase diagram of J1-J2 model on the cubic lattice

TL;DR

This study investigates the phase diagram of the J1-J2 Ising model on a cubic lattice, using Monte Carlo simulations to evaluate the accuracy of effective-field theory predictions and to analyze phase transition behaviors.

Contribution

It provides a numerical analysis of the phase diagram, clarifies the validity of EFT predictions, and identifies the universality class of the phase transition.

Findings

EFT predictions are qualitatively correct but show artifacts at low temperatures.

Reentrant behavior in the phase diagram is an artifact of EFT, not observed in Monte Carlo simulations.

The ferromagnetic to paramagnetic transition belongs to the 3D Ising universality class.

Abstract

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic nearest-neighbor interactions ($J_{1}$) and antiferromagnetic next-nearest-neighbor couplings ($J_{2}$) are analyzed in the plane temperature versus $\alpha$, where $\alpha=J_{2}/|J_{1}|$ is the frustration parameter. We used the original Wang-Landau sampling and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature reentrant behavior, observed in the frontier separating the ferromagnetic and the colinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo simulations of the model. In addition, our results indicate that the continuous phase transition between the Ferromagnetic and the Paramagnetic phases, that occurs for $0.0 \leq \alpha < 0.25$, belongs to the universality class of the three-dimensional pure Ising Model.