Mean-field phase diagram and spin glass phase of the dipolar Kagome Ising antiferromagnet

TL;DR

This paper presents a mean-field analysis of the phase diagram of a dipolar Kagome Ising antiferromagnet, revealing a crystalline phase and suggesting a spin glass transition that explains observed dynamical slowing down.

Contribution

It introduces a combined cluster variational Bethe-Peierls and cavity method approach to analyze the phase diagram of the dipolar Kagome Ising antiferromagnet at the mean-field level.

Findings

Confirmation of a weakly first-order crystalline phase transition.

Interpretation of dynamical slowing down as a spin glass transition.

Identification of a spin glass phase in the mean-field approximation.

Abstract

We derive the equilibrium phase diagram of the classical dipolar Ising antiferromagnet at the mean-field level on a geometry that mimics the two dimensional Kagome lattice. Our mean-field treatment is based on the combination of the cluster variational Bethe-Peierls formalism and the cavity method, developed in the context of the glass transition, and is complementary to the Monte Carlo simulations realized in [Phys. Rev. B 98, 144439 (2018)]. Our results confirm the nature of the low temperature crystalline phase which is reached through a weakly first-order phase transition. Moreover, they allow us to interpret the dynamical slowing down observed in the work of Hamp & al. as a remnant of a spin glass transition taking place at the mean-field level (and expected to be avoided in 2 dimensions).