Exponents appearing in the zero-temperature dynamics of the 1D Potts model

For the Glauber dynamics of the one-dimensional q-state Potts model at zero temperature, the fraction of spins which have never flipped up to time t decreases as t - theta (q ) where the exponent theta (q) varies continuously with q. The calculation of the q dependence of this exponent can be reduced to the study of a simple reaction-diffusion model. Using finite-size scaling, this allows one to obtain accurate estimates of B(q) for all values of q. One can also show that for 1=1+ epsilon , the expansion of theta (y) is given by theta (1)=(2/ pi ) epsilon +O( epsilon 2 ).