Emergent Critical Phase and Ricci Flow in a 2D Frustrated Heisenberg Model

TL;DR

This paper explores a 2D frustrated Heisenberg model revealing an emergent critical phase and connecting spin-stiffness scaling to Ricci flow, offering insights into complex magnetic behaviors.

Contribution

It introduces a novel 2D frustrated Heisenberg model and applies geometric Ricci flow analysis to understand its critical phenomena.

Findings

Identification of an emergent critical phase at low temperatures

Mapping of spin-stiffness scaling to Ricci flow equations

Description of a six-state clock model governing relative spin phases

Abstract

We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. Classically the two sublattices decouple, and "order from disorder" drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we show that the scaling of the spin-stiffnesses corresponds to the Ricci flow of a 4D metric tensor. At low temperatures, the relative phase between the spins on the two sublattices is described by a six-state clock model with an emergent critical phase.