Article Dans Une Revue Journal of Statistical Physics Année : 2005

Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales

Michel Bauer
Kalle Kytola
  • Fonction : Auteur
Denis Bernard

Résumé

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.

Dates et versions

hal-00023298 , version 1 (23-04-2006)

Identifiants

Citer

Michel Bauer, Kalle Kytola, Denis Bernard. Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales. Journal of Statistical Physics, 2005, 120, n°5_6, pp.1125 - 1163. ⟨10.1007/s10955-005-7002-5⟩. ⟨hal-00023298⟩
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