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Nonlinear Elastic Free Energies and Gradient Young-Gibbs Measures

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Abstract

We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations rate functional, is shown using a new interpolation lemma for partition functions. The local behaviour of the Gibbs measures can be parametrized by Young measures on the space of gradient Gibbs measures. In view of the unboundedness of the state space, the crucial tool here is an exponential tightness estimate that holds for a vast class of potentials and the construction of suitable compact sets of gradient Gibbs measures.

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Authors and Affiliations

  1. Department of Mathematics, University of Warwick, Coventry, UK

    Roman Kotecký

  2. Charles University, Prague, Czech Republic

    Roman Kotecký

  3. Institut für Mathematik, Leipzig University, 04009, Leipzig, Germany

    Stephan Luckhaus

Authors
  1. Roman Kotecký
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  2. Stephan Luckhaus
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Correspondence to Roman Kotecký.

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Communicated by H. Spohn

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Kotecký, R., Luckhaus, S. Nonlinear Elastic Free Energies and Gradient Young-Gibbs Measures. Commun. Math. Phys. 326, 887–917 (2014). https://doi.org/10.1007/s00220-014-1903-6

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  • DOI: https://doi.org/10.1007/s00220-014-1903-6

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