Monopole annihilation and causality

Abstract

It is shown that, contrary to a recent claim, causality alone does not impose any interesting constraints on the rate of monopole annihilation. We study a two-dimensional analog of the models in which monopoles get connected by strings and use a Monte Carlo simulation of the phase transitions to determine the length distribution of strings. The result is that long strings are exponentially suppressed. We then argue that for any initial length distribution of strings in two or three dimensions, an exponential distribution is eventually established by intercommutings or by spontaneous breaking of strings.