2002/12/20 by Frank O. Pfeiffer, Frank Pfeiffer, Heiko Rieger · 19 citations
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Critical exponent #Directed percolation #Electrical resistivity and conductivity #Lattice (music) #Loop (graph theory) #Material Dynamics and Properties #Mathematical physics #Mathematics #Mechanics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Phase transition #Physics #Quantum mechanics #Renormalization group #Square lattice #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Uncorrelated #Universality (dynamical systems) #Vortex #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.67.056113
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 67(5), 056113 (American Physical Society) · 8 pages, 8 figures
arxiv created 2002/12/20 · openalex publication_date 2003/05/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form a 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 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 universality class for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.