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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer Berlin Heidelberg

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10.1002/adma.200903097

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1432-0673

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Dobrushin States in the phi4 1 Model

Authors: Lorenzo Bertini Stella Brassesco Paolo Buttà
Publish Date: 2008/07/17
Volume: 190, Issue: 3, Pages: 477-516
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Abstract

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 phi4 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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  1. Optimal Design in Conductivity Under Locally Constrained Heat Flux
  2. Regularity Issues in the Problem of Fluid Structure Interaction
  3. Negative Eigenvalues of Two-Dimensional Schrödinger Operators
  4. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
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  6. Counterexamples to the Sonic Criterion
  7. Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution
  8. On Nonlinear Stochastic Balance Laws
  9. Weak Solutions of the Navier–Stokes Equations for Compressible Flows in a Half-Space with No-Slip Boundary Conditions
  10. Generalized Transition Fronts for One-Dimensional Almost Periodic Fisher-KPP Equations
  11. The Gel’fand Problem for the Biharmonic Operator
  12. The Existence Problem for Steiner Networks in Strictly Convex Domains
  13. Stability of Detonation Profiles in the ZND Limit
  14. Uniqueness of Absolute Minimizers for $${L^\infty}$$-Functionals Involving Hamiltonians $${H(x,p)}$$H(x,p)
  15. A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear Elastic Energy in Two Dimensions
  16. Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary
  17. The Toda System and Clustering Interfaces in the Allen–Cahn equation
  18. A Stability Criterion for Two-Fluid Interfaces and Applications
  19. Long-Time Convergence of an Adaptive Biasing Force Method: The Bi-Channel Case
  20. Displacement Convexity and Minimal Fronts at Phase Boundaries
  21. Gradient Bounds for Elliptic Problems Singular at the Boundary
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