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Percolation, Bose-Einstein condensation, and string proliferation
1Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, Finland.
Summary
Cluster percolation and string proliferation share critical phenomena analogies. String loop proliferation signals Bose-Einstein condensation or disordering, with critical exponents derived from loop distribution near criticality.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
Background:
- Percolation theory describes random systems.
- String theory involves worldlines and topological defects.
Purpose of the Study:
- To explore the analogy between cluster percolation and string proliferation.
- To understand critical phenomena in these systems.
Main Methods:
- Describing closed strings with a two-exponent distribution.
- Analyzing loop proliferation near critical points.
- Using the ideal Bose gas with a modified spectrum.
Main Results:
- Demonstrating a close analogy between cluster percolation and string proliferation.
- Showing string tension vanishes and loops proliferate at criticality.
- Linking loop proliferation to Bose-Einstein condensation or disordering.
Conclusions:
- General expressions for critical exponents were derived.
- The two-exponent parametrization effectively describes string behavior near criticality.
- The study provides insights into critical phenomena through this analogy.