We consider the hierarchical disordered pinning model studied in (
(1992) 1189–1213), which exhibits a localization/delocalization phase transition. In the case where the disorder is i.i.d. (independent and identically distributed), the question of relevance/irrelevance of disorder (i.e. whether disorder changes or not the critical properties with respect to the homogeneous case) is by now mathematically rather well understood (
(2010) 159–175,
(2010)...
Recently the renormalization group predictions on the effect of disorder on pinning models have been put on mathematical grounds. The picture is particularly complete if the disorder is or in the Harris criterion sense: the question addressed is whether quenched disorder leads to a critical behavior which is different from the one observed in the pure, i.e. annealed, system. The Harris criterion prediction is based on the sign of the specific heat exponent of the pure system, but it yields no...
We considerably improve upon the recent result of [37] on the mixing time of Glauber dynamics for the 2D Ising model in a box of side at low temperature and with random boundary conditions whose distribution stochastically dominates the extremal plus phase. An important special case is when is concentrated on the homogeneous all-plus configuration, where the mixing time is conjectured to be polynomial in . In [37] it was shown that for a large enough inverse-temperature and any there...
Consider the classical -dimensional Solid-On-Solid model above a hard wall on an box of . The model describes a crystal surface by assigning a non-negative integer height to each site in the box and 0 heights to its boundary. The probability of a surface configuration is proportional to , where is the inverse-temperature and sums the absolute values of height differences between neighboring sites. We give a full description of the shape of the SOS surface for low enough temperatures....
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