First-order transition in the stacked-$J_1$-$J_2$ Ising model on a cubic lattice

TL;DR

This study explores the phase transition nature of the stacked-$J_1$-$J_2$ Ising model on a cubic lattice, revealing a first-order transition for certain interaction ratios and contrasting theoretical predictions with Monte Carlo simulation results.

Contribution

It provides the first detailed analysis combining Monte Carlo simulations and renormalization group methods for this model, clarifying the transition order and critical exponents.

Findings

Identifies a first-order phase transition for $J_2/J_1>1/2$.

Shows critical exponents vary continuously between first-order and Ising values.

Excludes pseudo-first-order behavior in the studied parameter range.

Abstract

We investigate critical properties of the stacked-$J_1$-$J_2$ Ising model on a cubic lattice. Using Monte Carlo simulations and renormalization group, we find a single phase transition of the first order for $J_2/J_1>1/2$. The renormgroup approach predicts that a transition can be of the second order from the universality class of the $O(2)$ model, but the Monte Carlo results show another set of critical exponents: exponents continuously vary form the values typical for a first-order transition in the finite-size scaling theory at $1/2<J_2/J_1<1$ to the Ising values in the limit $J_2/J_1\to\infty$. We also exclude the pseudo-first-order behavior observed in the $J_1$-$J_2$ Ising model on a square lattice for $0.67\lesssim J_2/J_1\lesssim0.9$.