EXACT EXPONENT FOR THE NUMBER OF PERSISTENT SPINS IN THE ZERO-TEMPERATURE DYNAMICS OF THE ONE-DIMENSIONAL POTTS MODEL

摘要

For the zero-temperature Glauber dynamics of the q-state Potts model, the fraction r(q, t) of spins which never flip up to time t decays like a power law r(q, t) similar to t(-theta(q)) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A + A --> A) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of theta(q) for all values of q. The exponent theta(q) is in general irrational, theta(3) = 0.53795082..., theta(4) = 0.63151575..., ..., with the exception of q = 2 and q = infinity, for which theta(2) = 3/8 and theta(infinity) = 1. [References: 37]