PERCOLATION OF TERRACES, AND ENHANCEMENTS FOR THE ORTHANT MODEL

Abstract

We study a class of discrete geometric objects that we call terraces. These objects arise in, and are crucial for the study of phase transitions for a certain model of a random environment in general dimensions d ≥ 2. In this model, each lattice site is equipped with one of two local environments, with a parameter p governing the frequency of the first local environment. For each dimension d there is a critical parameter pc(d) at which a phase transition occurs for the connected cluster of sites that can be reached from the origin. We prove various results about local deformations of terraces, and subsequently apply the celebrated percolation theoretic methodology of enhancements in this nov..