Statistics of worMS and overlap loops in square lattice dimer model

Abstract

In this thesis, we discuss the non-intersecting loops formed by super-posing two random dimer configurations and how these are similar to contour lines of random gaussian surfaces. We specifically use a fully packed dimer cover of a square lattice and numerically try to find the exponents characterizing the distribution of subloops formed when two random dimer configurations are over-lapped. To generate a random dimer configuration we use the worm algorithm. We specify what the worm algorithm is and its relation to a random walk. We look at the probability distribution of the length of worms generated. To know more about the geometry of the worm, we look at the probability distribution of subloops that a worm breaks into. We find that these worms are non-markovian in nature and their subloops distribution show behavior similar to subloops generated in random dimer overlap.