Critical properties of loop percolation models with optimization constraints

Abstract

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional bond percolation. In contrast to this an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a new universality class, for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.

8 pages, 8 figures

References in corpus (13)

• Absence of a Phase Transition in a Three--Dimensional Vortex Glass Model with Screening
• Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-T_c Superconductors
• A Monte-Carlo Analysis of Percolation of Line-Segments on a Square Lattice
• Phase-coherence and the boson-analogy of vortex liquids
• Numerical Study of a Superconducting Glass Model
• Ground state properties of solid-on-solid models with disordered substrates
• Percolation, Bose-Einstein Condensation, and String Proliferation
• Application of a minimum cost flow algorithm to the three-dimensional gauge glass model with screening
• Statistical Topography of Glassy Interfaces
• Numerical study of the strongly screened vortex glass model in an external field
• Superconductor-to-Normal Phase Transition in a Vortex Glass Model: Numerical Evidence for a New Percolation Universality Class
• Universality and Critical Phenomena in String Defect Statistics
• Dislocations in the ground state of the solid-on-solid model on a disordered substrate

Cited by in corpus (12)

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• Negative-weight percolation
• The upper critical dimension of the negative-weight percolation problem
• Phase transitions in diluted negative-weight percolation models
• Site and bond percolation thresholds in $K_{n,n}$-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies
• Is negative-weight percolation compatible with SLE?
• Mean-field behavior of the negative-weight percolation model on random regular graphs
• The universality class of the continuous phase transition in the 2D "Touch and Stop" cluster growth percolation model
• Configurational statistics of densely and fully packed loops in the negative-weight percolation model
• Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6
• Percolation of satisfiability in finite dimensions
• Mixed-wet percolation on a dual square lattice