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- Title
Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales.
- Authors
Bauer, Michel; Bernard, Denis; Kytölä, Kalle
- Abstract
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conformal block is related to geometric configuration of the interfaces and what is the physical meaning of mixed conformal blocks. We illustrate the general ideas on concrete computations, with applications to percolation and the Ising model
- Subjects
MARTINGALES (Mathematics); STOCHASTIC processes; STATISTICAL mechanics; ISING model; ANALYTICAL mechanics
- Publication
Journal of Statistical Physics, 2005, Vol 120, Issue 5/6, p1125
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-005-7002-5