PMID: 11308550Apr 20, 2001Paper

Percolation, Bose-Einstein condensation, and string proliferation

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Adriaan M J Schakel

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 the case of worldlines) or the disordering of the ordered state (in the 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 parametrizing the loop distribution near criticality.

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Citations

Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·José A Cuesta, Richard P Sear
Jan 24, 2015·Physical Review Letters·Peter FinchJiannis K Pachos
Apr 28, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L ApoloA K Hartmann
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Frank O Pfeiffer, Heiko Rieger
Dec 13, 2006·Physical Review Letters·Daniel Ueltschi
Feb 18, 2019·Entropy·Alexander K HartmannChristoph Norrenbrock
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G ClaussenA K Hartmann
Apr 12, 2003·Physical Review Letters·H Kleinert, Adriaan M J Schakel

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