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Numerical Tests of Schramm-Loewner Evolution in Random Lattice Spin Models

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Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution

Part of the book series: Lecture Notes in Physics ((LNP,volume 853))

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Abstract

Interfaces induced by symmetry-breaking boundary conditions in lattice spin models are possible realisations of SLE. For homogeneous systems with short-ranged interactions, it can be shown, even rigorously in some cases, that the assumptions behind SLE (Domain Markov property and conformal invariance) hold true. However, this is not the case for random systems. In recent years, numerical simulations gave some evidences of a possible description of interfaces in random systems by SLE. Here, different numerical tests will be reviewed, both of the basic assumptions which underlie SLE and of several derived consequences of the SLE description of critical phenomena, which have been tried up to now. A detailed exposition of these evidences in the cases of the random Potts model, the Solid-On-Solid model on a random substrate and the 2D Ising spin glass will be provided.

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Authors and Affiliations

  1. GPS—DP2M—IJL (CNRS UMR 7198), Université de Lorraine Nancy, BP 70239, 54506, Vandœuvre-lès-Nancy Cedex, France

    Christophe Chatelain

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  1. Christophe Chatelain
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Correspondence to Christophe Chatelain .

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Editors and Affiliations

  1. CNRS - Nancy Université - UPVM, Dépt. de Physique de la Matière et des, Institut Jean Lamour, Vandoeuvre lès Nancy Cedex, 54506, France

    Malte Henkel

  2. IJL- Institut Jean Lamour- UMR 7198, Faculté des Sciences et Techniques, Nancy Université, Vandoeuvre-lès-Nancy Cedex, France

    Dragi Karevski

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Chatelain, C. (2012). Numerical Tests of Schramm-Loewner Evolution in Random Lattice Spin Models. In: Henkel, M., Karevski, D. (eds) Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution. Lecture Notes in Physics, vol 853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27934-8_3

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