Metastability cascades and prewetting in the SOS model

• 成果类型: Article
• 署名作者: Gheissari, Reza; Lubetzky, Eyal
• 署名单位: Northwestern University; New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01328-7
• 发表日期: 2025
• 页码: 1485-1556
• 关键词: kosterlitz-thouless transition; layering transition; spin systems; ising-model; surface; interface; wall; fluctuations; equilibrium; DYNAMICS

摘要

We study Glauber dynamics for the low temperature (2 +1)D Solid-On-Solid model on a box of side-length n with a floor at height 0 (inducing entropic repulsion) and a competing bulk external field lambda pointing down (the prewetting problem). In 1996, Cesi and Martinelli showed that if the inverse-temperature beta is large enough, then along a decreasing sequence of critical points (lambda((k)K beta)(c)(k=0) the dynamics is torpid: its inverse spectral gap is O(1) when lambda is an element of (lambda((k + 1))(c),lambda((k))(c)) whereas it is exp[Theta (n)] at each lambda((k))(c) for each k <= K-beta, due to a coexistence of rigid phases at heights k + 1 and k. Our focus is understanding (a) the onset of metastability as lambda(n) up arrow lambda((k))(c) ; and (b) the effect of an unbounded number of layers, as we remove the restriction k <= K-beta, and even allow for lambda(n) -> 0 towards the lambda = 0 case which has layers and was studied by Caputo et al. (Ann Probab 42(4):1516-1589, 2014). We show that for any k, possibly growing with n, the inverse gap is exp[Theta (l/ lambda(n) - lambda((k))(c)|)] as lambda up arrow lambda((k))(c) up to distance n(-1+0(1))from this critical point, due to a metastable layer at height k on the way to forming the desired layer at height k + 1. By taking lambda(c) = n(-alpha)(corresponding to k(n) asymptotic to log n), this also interpolates down to the behavior of the dynamics when lambda = 0. We complement this by extending the fast mixing to all uniformly bounded away from lambda((k))(c))(infinity)(k=0). Together, these results provide a sharp understanding of the predicted infinite sequence of dynamical phase transitions governed by the layering phenomenon.