Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

Abstract

Critical and in the highly frustrated regime also dynamical properties of the $J_1-J_2$ Ising model with competing nearest-neighbor $J_1$ and second-nearest-neighbor $J_2$ interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within $R\equiv J_2/|J_1|\in [-1/4,0]$. It is confirmed that at least for $R\ge -0.2$ the transition remains second-order and complies with the standard Ising universality class. In the highly frustrated regime of $R<-0.2$ and low temperatures the system tends to freeze to metastable domain states, separated by large energy barriers, which show extremely sluggish dynamics. The resulting huge equilibration and autocorrelation times hinder the analysis of critical properties and thus the character of the transition in this region remains to be determined.

10 pages, 4 figures

References in corpus (5)

• Phase diagram of the Ising square lattice with competing interactions
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Phase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning
• Phase transitions in a frustrated Ising antiferromagnet on a square lattice
• Nematic phase in the J${}_1$-J${}_2$ square lattice Ising model in an external field

Cited by in corpus (4)

• Emergent ${\mathbb{Z}}_2$ gauge theories and topological excitations in Rydberg atom arrays
• Spiral-spin-liquid behaviors and persistent reciprocal kagomé structure in frustrated van der Waals magnets and beyond
• The frustrated Ising model on the body-centered cubic lattice
• Frustrated Ising model on the honeycomb lattice: Metastability and universality