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Quasi-polynomial mixing of the 2D stochastic Ising model with “plus” boundary up to criticality

Eyal LubetzkyFabio MartinelliAllan SlyFabio Lucio Toninelli — 2013

Journal of the European Mathematical Society

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 L at low temperature and with random boundary conditions whose distribution P stochastically dominates the extremal plus phase. An important special case is when P is concentrated on the homogeneous all-plus configuration, where the mixing time T M I X is conjectured to be polynomial in L . In [37] it was shown that for a large enough inverse-temperature β and any ϵ > 0 there...

Scaling limit and cube-root fluctuations in SOS surfaces above a wall

Pietro CaputoEyal LubetzkyFabio MartinelliAllan SlyFabio Lucio Toninelli — 2016

Journal of the European Mathematical Society

Consider the classical ( 2 + 1 ) -dimensional Solid-On-Solid model above a hard wall on an L × L box of 2 . The model describes a crystal surface by assigning a non-negative integer height η x to each site x in the box and 0 heights to its boundary. The probability of a surface configuration η is proportional to exp ( - β ( η ) ) , where β is the inverse-temperature and ( η ) 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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