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Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales

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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

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Authors and Affiliations

  1. Service de Physique Théorique de Saclay, CEA/DSM/SPhT, Unité de recherche associée au CNRS, CEA-Saclay, Gif-sur-Yvette, 91191, France

    Michel Bauer & Denis Bernard

  2. Department of Mathematics, University of Helsinki, P.O. Box 68, FIN 00014, Finland

    Kalle Kytölä

Authors
  1. Michel Bauer
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  2. Denis Bernard
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  3. Kalle Kytölä
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Correspondence to Denis Bernard.

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Bauer, M., Bernard, D. & Kytölä, K. Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales. J Stat Phys 120, 1125–1163 (2005). https://doi.org/10.1007/s10955-005-7002-5

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  • DOI: https://doi.org/10.1007/s10955-005-7002-5

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