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The Raise and Peel Model of a Fluctuating Interface

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Abstract

We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some interesting features. For example, the spectrum is given by conformal field theory, and the stationary non-equilibrium probability distribution is given by the two-dimensional equilibrium distribution of the ice model with domain wall type boundary conditions. This connection is used to find exact analytic expressions for several quantities of the stochastic model. Vice versa, some understanding of the ice model with domain wall type boundary conditions can be obtained by the study of the stochastic model. At the special point we study several properties of the model, such as the height fluctuations as well as cluster and avalanche distributions. The latter has a long tail which shows that the model exhibits self organized criticality. We also find in the stationary state a special surface phase transition without enhancement and with a crossover exponent φ=2/3. Furthermore, we study the phase diagram of the model as a function of the adsorption rate and find two massive phases and a scale invariant phase where conformal invariance is broken.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, 3010, Australia

    Jan de Gier, Paul A. Pearce & Vladimir Rittenberg

  2. Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE, Amsterdam, The Netherlands

    Bernard Nienhuis

  3. Physikalisches Institut, Bonn University, 53115, Bonn, Germany

    Vladimir Rittenberg

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  1. Jan de Gier
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  2. Bernard Nienhuis
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  3. Paul A. Pearce
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  4. Vladimir Rittenberg
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de Gier, J., Nienhuis, B., Pearce, P.A. et al. The Raise and Peel Model of a Fluctuating Interface. Journal of Statistical Physics 114, 1–35 (2004). https://doi.org/10.1023/B:JOSS.0000003102.81727.fd

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