Dobrushin states in the φ^4_1 model

Details Dobrushin states in the φ^4_1 model Dobrushin states in the φ^4_1 model

2006-11-27

arxiv.org/abs/math-ph/0611077v1

Arch. Rational Mech. Anal.190:477-516,2008

Physics

Mathematical Physics

34 pages

Scientific paper

10.1007/s00205-008-0151-3

We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic free energy cost, as the length of the interval diverges, of shifting the interface from the midpoint. We then discuss the effect of thermal fluctuations by analyzing the \phi^4_1-measure with Dobrushin boundary conditions. In particular, we obtain a nontrivial limit in a suitable scaling in which the length of the interval diverges and the temperature vanishes. The limiting state is not translation invariant and describes a localized interface. This result can be seen as the probabilistic counterpart of the variational convergence of the associated excess free energy.

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