Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales

By Michel Bauer, D. Bernard, Kalle Kytölä. 2005

180 citations recorded by the source corpus.

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

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d488dd0295df54cef2d72ea1f1c420eee2b50ac2

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Citations in the corpus

The configurational measure on mutually avoiding SLE paths (2006, background): “For a statistical mechanics argument describing multiple SLEs, consult [1].”
2D growth processes: SLE and Loewner chains (2006, methodology): “fact symmetric. This is closely related to the general deﬁnition of multiple SLE’s, either by imposing commutativity [47] or by imposing properties natural from the viewpoint of statistical mechanics [13]. 2.4 Other growth processes Previous examples, either geometrical or extracted from statistical”
Universality in the 2D Ising model and conformal invariance of fermionic observables (2009, methodology): “The version of this formula for multiple SLEs was derived by Bauer, Bernard and Kytölä in [1], see page 1160, their notation for the modulus related to ours by x = 1 − u.”