Percolation, Bose-Einstein Condensation, and String Proliferation

Details Percolation, Bose-Einstein Condensation, and String Proliferation Percolation, Bose-Einstein Condensation, and String Proliferation

2000-08-30

arxiv.org/abs/cond-mat/0008443v1

Phys.Rev.E63:026115,2001

Physics

Condensed Matter

12 pages, 3x2 figures

Scientific paper

10.1103/PhysRevE.63.026115

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.

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