Plaquette Ising models, degeneracy and scaling

Johnston, D.A.; Mueller, Marco; Janke, Wolfhard

doi:10.1140/epjst/e2016-60329-4

Cited by 30 publications

(26 citation statements)

References 76 publications

(125 reference statements)

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“…The resulting theory turned out to be dual to a non-gauge theory of N spins interacting around a plaquette [3]. These theories are known as Ising-plaquette theories and they had been studied extensively (see [32] for a review and references therein).…”

Section: )mentioning

confidence: 99%

Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2020

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We extend our exploration of nonstandard continuum quantum field theories in 2+12+1 dimensions to 3+13+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1)U(1) symmetry and in a followup paper we will study models with a global \mathbb{Z}_NℤN symmetry.

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Section: )mentioning

confidence: 99%

Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2020

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“…Euclidean Path Integral and Wilson Loops for Plaquette Gauge Theory .-We will now proceed with our analysis of the "plaquette gauge theory" (PGT), which arises from applying the generalized gauging procedure to the classical plaquette Ising model 6,7,38 and produces X-cube fracton topological order in its deconfined phase, by analogy with the IGT of the preceding section. The main deviation from the standard gauging procedure is that we place σ at the center of each interaction in the Hamiltonian (the plaquettes in this model), rather than always on the links (these are the "nexus" spins of Ref.…”

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confidence: 99%

Correlation function diagnostics for type-I fracton phases

2018

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Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional subspaces, including the eponymous fractons that are immobile in isolation. We develop correlation function diagnostics to characterize Type I fracton phases which build on their exhibiting partial deconfinement. These are inspired by similar diagnostics from standard gauge theories and utilize a generalized gauging procedure that links fracton phases to classical Ising models with subsystem symmetries. En route, we explicitly construct the spacetime partition function for the plaquette Ising model which, under such gauging, maps into the X-cube fracton topological phase. We numerically verify our results for this model via Monte Carlo calculations.

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“…As the system changes from the solidlike into the columnar phase, simulations show clear signs of a first-order phase transition. From finite-size scaling analysis, we find a nonstandard relation predicted by a number of recent studies [43,44,51] where physical quantities scale with L 1 instead of the standard L 2 . Whether this scaling is due to the close-packed configuration degeneracy exponentially growing with system size or due to surface interactions in the domains phase still not clear.…”

Section: Discussionmentioning

confidence: 57%

“…Therefore, we proceed as in Ref. [44] and adjust values of critical chemical potential obtained by the maximum of the order parameter susceptibility, μ χ (L), to the following scaling law…”

Section: B Up To Second-neighbors Exclusion (K = 2)mentioning

confidence: 99%

Phase transitions in hard-core lattice gases on the honeycomb lattice

Thewes

Fernandes

2020

Phys. Rev. E

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We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order k (k = 1,. .. , 5) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first-neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the two-dimensional Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high-density columnar phase undergoes a first-order phase transition with nonstandard scaling to a solidlike phase with short-range ordered domains and, then, to fluidlike configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the three-state Potts model. The 5NN system undergoes two first-order phase transitions, both with nonstandard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

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Plaquette Ising models, degeneracy and scaling

Cited by 30 publications

References 76 publications

Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Correlation function diagnostics for type-I fracton phases

Phase transitions in hard-core lattice gases on the honeycomb lattice

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