94-406 Cesi F, Martinelli F
On the Layering Transition of an SOS Surface Interacting with a Wall. I. Equilibrium Results (194K, TeX) Dec 23, 94
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider the model of a 2D surface above a fixed wall and attracted towards it by means of a positive magnetic field $h$ in the solid on solid (SOS) approximation, when the inverse temperature $\beta$ is very large and the external field $h$ is exponentially small in $\b$. We improve considerably previous results by Dinaburg and Mazel on the competition between the external field and the entropic repulsion with the wall, leading, in this case, to the phenomenon of layering phase transitions. In particular we show, using the Pirogov Sinai scheme as given by Zahradn\'\i k, that there exists a unique critical value $h^*_k(\beta)$ in the interval $({1\over 4}e^{-4\beta k}, 4e^{-4\beta k})$ such that, for all $h\in (h^*_{k+1},h^*_k)$ and $\beta$ large enough, there exists a unique infinite volume Gibbs state. The typical configurations are small perturbations of the ground state represented by a surface at height $k+1$ above the wall. Moreover, for the same choice of the thermodynamic parameters, the influence of the boundary conditions of the Gibbs measure in a finite cube decays exponentially fast with the distance from the boundary. When $h=h^*_k(\beta)$ we prove instead the convergence of the cluster expansion for both $k$ and $k+1$ boundary conditions. This fact signals the presence of a phase transition. In the second paper of this series we will consider a Glauber dynamics for the above model and we will study the rate of approach to equilibrium in a large finite cube with arbitrary boundary conditions as a function of the external field $h$. Using the results proven in this paper we will show that there is a dramatic slowing down in the approach to equilibrium when the magnetic field takes one of the critical values and the boundary conditions are free (absent).

Files: 94-406.tex