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

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 $0.67\lesssim J_2/J_1\lesssim 0.9$.

arXiv comment6 pages, 6 figures

References in corpus (16)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• The critical behavior of frustrated spin models with noncollinear order
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Location of the Potts-critical end point in the frustrated Ising model on the square lattice
• Criticality versus q in the 2+1-dimensional $Z_q$ clock model
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
• Monte Carlo study of very weak first-order transitions in the three-dimensional Ashkin-Teller model
• Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models
• Monte Carlo study of the Pure and Dilute Baxter-Wu model
• Functional renormalization group approach to non-collinear magnets
• Monte Carlo study of the critical properties of noncollinear Heisenberg magnets: $O(3)\times O(2)$ universality class
• Critical and multicritical behavior in the Ising-Heisenberg universality class
• Determination of CFT central charge by the Wang-Landau algorithm
• First-order and pseudo-first-order transition in the high dimensional $O(N)\otimes O(M)$ model