Plaquette Ising models, degeneracy and scaling

TL;DR

This paper reviews recent findings on the 3D plaquette Ising model, highlighting its unique phase transition, unusual scaling behavior due to degeneracy, and implications for magnetic order and fracton topological defects.

Contribution

It provides a comprehensive review of the unusual scaling properties and degeneracy effects in the 3D plaquette Ising model, including its impact on magnetic order and topological defects.

Findings

First-order phase transition with unusual 1/L^2 scaling correction

Degeneracy leads to intermediate magnetic order

Presence of fracton topological defects in related quantum models

Abstract

We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the leading scaling correction is modified from the usual inverse volume behaviour 1/L^3 to 1/L^2. The degeneracy also has implications for the magnetic order in the model which has an intermediate nature between local and global order and gives rise to novel fracton topological defects in a related quantum Hamiltonian.