Location of the Potts-critical end point in the frustrated Ising model on the square lattice

Abstract

We report on Monte Carlo simulations for the two-dimensional frustrated $J_1$-$J_2$ Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear state different phase-transition scenarios apply depending on the value of the frustration $J_2/J_1$. In particular a region with critical Ashkin-Teller-like behavior, i.e., a second-order phase transition with varying critical exponents, and a noncritical region with first-order indications were verified. However, the exact transition point $[J_2/J_1{]}_C$ between both scenarios was under debate. In this paper we present Monte Carlo data which strengthens the conclusion of Jin \et [Phys. Rev. Lett. \textbf{108}, 045702 (2012)] that the transition point is at a value of $J_2/J_1\approx 0.67$ and that double-peak structures in the energy histograms for larger values of $J_2/J_1$ are unstable in a scaling analysis.

4 pages, 6 figures

References in corpus (7)

• Feedback-optimized parallel tempering Monte Carlo
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Critical Binder cumulant in two-dimensional anisotropic Ising models
• Phase diagram of the Ising square lattice with competing interactions
• Gauge theory picture of an ordering transition in a dimer model
• Critical Binder cumulant of two-dimensional Ising models
• Monte Carlo studies of the Ising square lattice with competing interactions

Cited by in corpus (20)

• Exploring neural network training strategies to determine phase transitions in frustrated magnetic models
• Phase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning
• Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Field-tunable interactions and frustration in underlayer-mediated artificial spin ice
• The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
• Antiferromagnetic triangular Blume-Capel model with hard core exclusions
• Ashkin-Teller criticality and weak-first-order behavior of phase transition to four-fold degenerate state in two-dimensional frustrated Ising antiferromagnets
• The frustrated Ising model on the body-centered cubic lattice
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Phase determination with and without deep learning
• Critical behavior of a 2D spin-pseudospin model in a strong exchange limit
• Stripe order, impurities, and symmetry breaking in a diluted frustrated magnet
• Comments on the minimal training set for CNN: a case study of the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Critical properties of a 2D frustrated magnet with non-magnetic impurities
• First-order transition in the stacked-$J_1$-$J_2$ Ising model on a cubic lattice
• Nontrivial Ground State Degeneracy of the Spin-Pseudospin Model of a Two-Dimensional Magnet Near the Frustration Point
• Frustrated Ising model on the honeycomb lattice: Metastability and universality
• Stripe order in quasicrystals
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions