期刊
JOURNAL OF STATISTICAL PHYSICS
卷 155, 期 6, 页码 1222-1248出版社
SPRINGER
DOI: 10.1007/s10955-014-0945-7
关键词
Random permutations; Infinite volume limit; Kosterlitz-Thouless transition; Fractal dimension; Schramm-Lowner evolution
Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary conditions, we prove existence of the infinite volume limit under fairly weak assumptions. When the dimension of the lattice is two, we give numerical evidence of a Kosterlitz-Thouless transition, and of long cycles having an almost sure fractal dimension in the scaling limit. Finally we comment on possible connections to Schramm-Lowner curves.
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