Plaquette Ising models, degeneracy and scaling

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.

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• A Modified Villain Formulation of Fractons and Other Exotic Theories
• Correlation function diagnostics for type-I fracton phases
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• More Exotic Field Theories in 3+1 Dimensions
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Spontaneously Broken Subsystem Symmetries
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• Fractons and exotic symmetries from branes
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Foliated-Exotic Duality in Fractonic BF Theories
• Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
• Linked Cluster Expansions via Hypergraph Decompositions
• Foliated order parameter in a fracton phase transition
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Hybrid Symmetry Breaking in Classical Spin Models With Subsystem Symmetries
• The statistics of the ordering of chiral ribbons on a honeycomb lattice