On the Ising model with random boundary condition

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.

55 pages, minor corrections and 7 figures added, to appear in J. Stat. Phys

References in corpus (5)

• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Nonrealistic Behavior of Mean Field Spin Glasses
• Renormalization Group in the uniqueness region: weak Gibbsianity and convergence
• Graded cluster expansion for lattice systems
• Infinitely many states and stochastic symmetry in a Gaussian Potts-Hopfield model

Cited by in corpus (6)

• A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model
• Two connections between random systems and non-Gibbsian measures
• Incoherent boundary conditions and metastates
• Examples of DLR states which are not weak limits of finite volume Gibbs measures with deterministic boundary conditions
• Infinite volume Gibbs states and metastates of the random field mean-field spherical model
• Griffiths-type theorems for short-range spin glass models