Damage spreading in two dimensional geometrically frustrated lattices: the triangular and kagome anistropic Heisenberg model

TL;DR

This paper uses damage spreading to explore phase diagrams of anisotropic Heisenberg antiferromagnets on triangular and kagome lattices, revealing distinct phase transitions consistent with Monte Carlo results.

Contribution

It applies damage spreading to frustrated lattices, identifying phase boundaries and transitions, including Kosterlitz-Thouless and glassy transitions, with validation against Monte Carlo simulations.

Findings

Triangular lattice exhibits two Kosterlitz-Thouless transitions.

Kagome lattice undergoes a glassy transition.

Damage spreading phase boundaries agree with Monte Carlo results.

Abstract

The technique of damage spreading is used to study the phase diagram of the easy axis anisotropic Heisenberg antiferromagnet on two geometrically frustrated lattices. The triangular and kagome systems are built up from triangular units that either share edges or corners respectively. The triangular lattice undergoes two sequential Kosterlitz-Thouless transitions while the kagome lattice undergoes a glassy transition. In both cases, the phase boundaries obtained using damage spreading are in good agreement with those obtained from equilibrium Monte Carlo simulations.