Grassmann Path Integral Approach to Two-Dimensional Percolation Near the Critical Point

Abstract

The concept of percolation is a fundamental one in the physics of disordered systems and has been discussed at length at this Institute. Over the last decade, a consistent theory of percolation has emerged, borrowing heavily from the familiar description of critical phenomena. In particular, in two dimensions (2D) a small set of plausible assumptions has led to a conjectured exact theory for the asymptotic behaviour near the percolation threshold, p_c.[1] Central amongst these is the assumption that the critical singularities are in the form of power laws.