# Spin-glass-like ordering in a frustrated $J_1-J_2$ Ising antiferromagnet on a honeycomb lattice

## TL;DR

This study investigates the low-temperature phase of a frustrated honeycomb-lattice Ising model with competing interactions, revealing a spin-glass-like phase with frozen domains and no long-range magnetic order for certain interaction ratios.

## Contribution

It uncovers a novel spin-glass-like phase in the frustrated honeycomb Ising model for $R > 1/4$, characterized by frozen domains and absence of long-range order, using Monte Carlo simulations.

## Key findings

- Existence of a spin-glass-like phase with frozen domains.
- No conventional long-range magnetic order for $R > 1/4$.
- Detection of a phase transition associated with domain freezing.

## Abstract

We study the nature of a low-temperature phase in the frustrated honeycomb-lattice Ising model with first- and second-neighbor antiferromagnetic (AF) interactions, $J_1$ and $J_2$, respectively, for $R = J_2/J_1 > 1/4$. It is known that for $R < 1/4$ there is a phase transition at low temperatures to the AF phase. Nevertheless, little is known about the critical behavior of the model for $R > 1/4$, except for recent effective field results which detected no phase transition down to zero temperature. Our Monte Carlo results suggest that for $R > 1/4$ there is at least one peculiar phase transition accompanied by a spin-glass-like freezing to a highly degenerate state consisting of frozen domains with stripe-type AF ordering separated by zero-energy domain walls. In spite of the local ordering within the respective domains there is no ordering among them and thus, unlike in the corresponding square-lattice model with $R > 1/2$, there is no conventional magnetic long-range ordering spanning the entire system.