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On the Ising Model with Random Boundary Condition

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Abstract

The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the ‘+’ and ‘−’ phases are the only almost sure limit Gibbs measures, assuming that the limit is taken along a sparse enough sequence of squares. In particular, we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces. In order to exclude mixtures as possible limit points, a detailed multi-scale contour analysis is performed.

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Author notes

  1. K. Netočný

    Present address: Institute for Theoretical Physics, University of Groningen, The Netherlands

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Groningen, The Netherlands

    A. C. D. van. Enter & H. G. Schaap

  2. Eurandom, Eindhoven, The Netherlands

    K. Netočný

  3. Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    K. Netočný

Authors
  1. A. C. D. van. Enter
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  2. K. Netočný
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  3. H. G. Schaap
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Correspondence to A. C. D. van. Enter.

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Enter, A.C.D.v., Netočný, K. & Schaap, H.G. On the Ising Model with Random Boundary Condition. J Stat Phys 118, 997–1056 (2005). https://doi.org/10.1007/s10955-004-2138-2

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