THE FINITE-TEMPERATURE PHASE-TRANSITION OF SU(2) GAUGE-FIELDS IN 2+1 DIMENSIONS

We perform finite temperature simulations of SU(2) lattice gauge field s in two spatial dimensions. We calculate the correlation length and f ind that it appears to diverge at a critical temperature, indicating a second order phase transition. Our average value for the associated c ritical exponent is gamma = 0.975(-0.035)+0.045 which is consistent wi th the value gamma = 1 in the D = 2 Ising model. We calculate the crit ical temperature, T(c), in units of the string tension, sigma, and ext rapolate to the continuum limit. If we use the theoretically favoured value, gamma = 1, in our fits for T(c) then we obtain T(c)/square-root sigma = 1.121 +/- 0.008. If, instead, we allow y to be free then we o btain a somewhat less precise value: T(c)/square-root sigma = 1.118(-0 .016)+0.034. We note that while this value is very different from the corresponding value in four dimensions, most of the difference can be understood on simple dimensional grounds.