(Four) Dual Plaquette 3D Ising Models
arXiv:2006.05377 · doi:10.3390/e22060633
Abstract
A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3d plaquette Ising and the X-Cube model is similar to that between the 2d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.
arXiv commentReviews results in arXiv:1106.0325 and arXiv:1106.4664 in light of more recent simulations and fracton literature. Published in special issue of Entropy dedicated to the memory of Professor Ian Campbell
References in corpus (40)
- Fault-tolerant quantum computation by anyons
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- Fractons
- Fracton Phases of Matter
- Glassy quantum dynamics in translation invariant fracton models
- Three-Dimensional 3-State Potts Model Revisited With New Techniques
- Geometrical String and Spin Systems
- Gonihedric String and Asymptotic Freedom
- Novel glassy behavior in a ferromagnetic p-spin model
- Self-Avoiding Gonihedric Srting and Spin Systems
- Interaction Hierarchy
- Cooling-rate effects in a model of (ideal?) glass
- Fractons from confinement in one dimension
- String fine tuning
- Slow dynamics of Ising models with energy barriers
- Phase Transition in Lattice Surface Systems with Gonihedric Action
- Interaction Hierarchy. Gonihedric String and Quantum Gravity
- GEOMETRICAL STRING and DUAL SPIN SYSTEMS
- Glassy transition and metastability in four-spin Ising model
- Evidence for a first order transition in a plaquette 3d Ising-like action
- Non-Standard Finite-Size Scaling at First-Order Phase Transitions
- Glassy dynamics, metastability limit and crystal growth in a lattice spin model
- Low temperature expansion of the gonihedric Ising model
- Dual Statistical Systems and Geometrical String
- Gonihedric 3D Ising Actions
- Two and Three-Dimensional Spin Systems with Gonihedric Action
- String tension in gonihedric 3D Ising models
- Gonihedric (and Fuki-Nuke) Order
- Phase structure of four-dimensional gonihedric spin system
- Monopole clusters, center vortices, and confinement in a Z(2) gauge-Higgs system
- Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
- Odd Fracton Theories, Proximate Orders, and Parton Constructions
- Four-dimensional gonihedric gauge spin system
- Three-dimensional gonihedric spin system
- Alternative actions for quantum gravity and the intrinsic rigidity of the spacetime
- New Random Ordered Phase in Isotropic Models with Many-body Interactions
- A pedagogical overview on 2D and 3D Toric Codes and the origin of their topological orders
- The Dual Gonihedric 3D Ising Model
- Planar ordering in the plaquette-only gonihedric Ising model
- Transmuted finite-size scaling at first-order phase transitions