Percolation, Bose-Einstein Condensation, and String Proliferation

Abstract

The close analogy between cluster percolation and string proliferation in the context of critical phenomena is studied. Like clusters in percolation theory, closed strings, which can be either finite-temperature worldlines or topological line defects, are described by a distribution parametrized by only two exponents. On approaching the critical point, the string tension vanishes, and the loops proliferate thereby signalling the onset of Bose-Einstein condensation (in case of worldlines) or the disordering of the ordered state (in case of vortices). The ideal Bose gas with modified energy spectrum is used as a stepping stone to derive general expressions for the critical exponents in terms of the two exponents parameterizing the loop distribution near criticality.

12 pages, 3x2 figures

References in corpus (4)

• Hausdorff dimension of critical fluctuations in abelian gauge theories
• O(2) symmetry breaking vs. vortex loop percolation
• Cluster Percolation in O(n) Spin Models
• String Picture of Bose-Einstein Condensation

Cited by in corpus (21)

• Percolation transition in the Bose gas II
• Geometrical vs. Fortuin-Kasteleyn Clusters in the Two-Dimensional $q$-State Potts Model
• Towards understanding structure of the monopole clusters
• Quantum magnetic monopole condensate
• Long Cycles in a Perturbed Mean Field Model of a Boson Gas
• The relation between Feynman cycles and off-diagonal long-range order
• Critical properties of loop percolation models with optimization constraints
• Negative-weight percolation
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network
• Vortex-line percolation in the three-dimensional complex |psi|^4 model
• Phase transitions in diluted negative-weight percolation models
• Gauge-invariant critical exponents for the Ginzburg-Landau model
• Magnetic component of gluon plasma and its viscosity
• Geometrical Phase Transitions
• Induced topological order at the boundary of 3D topological superconductors
• Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6
• Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores
• Critical point influenced by Bose-Einstein condensation
• Infinite Cycles in Boson Lattice Models
• Simultaneous occurrence of off-diagonal long-range order and infinite permutation cycles in systems of interacting atoms