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(Four) Dual Plaquette 3D Ising Models.

Desmond A Johnston¹, Ranasinghe P K C M Ranasinghe²

¹School of Mathematical and Computer Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK.

Entropy (Basel, Switzerland)

|December 8, 2020

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This study explores the classical spin version of a 3D plaquette Ising model, revealing its connections to fracton models and dual formulations. The research clarifies relationships between different spin models and their duals, including the X-Cube and Ashkin-Teller models.

Area of Science:

Condensed Matter Physics
Quantum Information Theory

Background:

The 3D plaquette Ising model possesses planar subsystem symmetry, a key feature distinguishing it from other models.
The quantum version of this model is dual to the X-Cube model, a foundational model in fracton physics.
This duality is analogous to the 2D Ising model's relation to the Toric Code, achieved through gauging symmetries.

Purpose of the Study:

To investigate the classical spin version of a non-standard dual Hamiltonian for the 3D plaquette Ising model.
To explore the properties of this classical dual and its relationship with other dual formulations.
To understand the connections between fracton models and Ising-type models through duality.

Main Methods:

Investigation of a classical spin Hamiltonian derived from a non-standard dual formulation.

Keywords:

Ising model fractons statistical mechanics

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Analysis of the properties of this classical dual Hamiltonian.

Comparison with established dual formulations, including Ashkin-Teller-like models and vertex/link spin models.

Main Results:

The classical spin version of the non-standard dual Hamiltonian exhibits properties related to fracton physics.
New insights into the dualities between 3D plaquette Ising models and X-Cube models are provided.
Connections are established between different dual formulations, involving various spin types and lattice structures.

Conclusions:

The classical spin dual of the 3D plaquette Ising model offers a valuable perspective on fracton physics.
Understanding these dualities deepens our knowledge of topological phases and their underlying symmetries.
The study highlights the rich landscape of dualities in statistical mechanics and quantum field theory.