# Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets

## TL;DR

This study investigates the robustness of entropy plateaus in triangular Ising antiferromagnets, revealing they are sensitive to interaction strength and disorder, which explains their rarity in experiments.

## Contribution

The paper provides a detailed numerical analysis showing how second-neighbor interactions and disorder affect the existence of entropy plateaus in TIAF.

## Key findings

- Entropy plateaus exist only with weak second-neighbor interactions.
- Disorder in exchange interactions easily destroys entropy plateaus.
- Experimental absence of plateaus explained by interaction strength and disorder sensitivity.

## Abstract

Residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-$Z_2$-flux variables in Kitaev models, the freezing of one set of degrees of freedom and establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO$_4$ by Li et al, we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. We find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.