On gonihedric loops and quantum gravity

Espriu, D.; Prats, Alberto

doi:10.1088/0305-4470/39/7/017

Cited by 3 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The model is shown to have 1d subsystem symmetry [53,62] and thus considered as a model for fracton-like order [49,50] as we will see. Its classical version is known as the gonihedric Ising model, a particular case of the eight-vertex model [50,63], studied in the context of string theory and spinglass physics in [64][65][66][67] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Fracton-like phases from subsystem symmetries

Ibieta-Jimenez,

Xavier,

Petrucci

et al. 2019

Preprint

View full text Add to dashboard Cite

We study models with fracton-like order based on Z2 lattice gauge theories with subsystem symmetries in d = 2 and d = 3 spatial dimensions. The 3d model reduces to the 3-dimensional Toric Code when subsystem symmetry is broken. Although not topologically protected, its ground state degeneracy has as leading contribution a term which grows exponentially with the square of the linear size of the system. Also, there are completely mobile gauge charges living along with immobile fractons. Until now most fracton models were obtained from a process of gauging subsystem symmetries of some generalized Abelian lattice gauge theories, and our method shows that fracton-like phases are also present in more usual lattice gauge theories. We calculate the entanglement entropy SA of these models in a sub-region A of the lattice and show that it is equal to the logarithm of the ground state degeneracy of a particular restriction of the full model to A. We also show how to construct models with fracton-like order from lattice gauge theories with arbitrary, possibly non-Abelian finite gauge groups and as examples, we study some models obtained from choosing Z3 and S3 as gauge groups.

show abstract

Section: Introductionmentioning

confidence: 99%

Fracton-like phases from subsystem symmetries

Ibieta-Jimenez,

Xavier,

Petrucci

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

The Gonihedric Ising Model and Glassiness

Johnston

Lipowski

Malmini

Rugged Free Energy Landscapes

View full text Add to dashboard Cite

(Pre-)History of the ModelThe Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and − spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum.The model is a generalised Ising model living on a cubic 3D lattice with nearest neighbour, next to nearest-neighbour and plaquette interactions. The ratio between the couplings of these three terms is fixed to a one parameter family which endows the model with unusual properties both in and out of equilibrium. Of particular interest for the discussion here will be that the model manifests all the indications of glassy behaviour without any recourse to quenched disorder, whilst still possessing a crystalline low temperature phase in equilibrium.In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to the investigation of the non-equilibrium, glassy behaviour of the model. We apologize in advance for our narrow focus on things Gonihedric at the expense of other lattice models with glassy behaviour, since the aim is to concentrate on giving an overview of the Gonihedric Ising model in 3D.The model has an unusual genesis since it was originally introduced as a potential discretization of string theory. The Nambu-Goto [1] action (or Hamiltonian in statistical mechanical language) in bosonic string theory is given by the area swept out by the string worldsheet as it moves through spacetime. Directly discretizing euclideanized versions of this action produced ensembles of surfaces, i.e. string worldsheets, which were dominated by collapsed and irregular configurations such as that in Fig.1 and which were unsuitable for

show abstract