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

We perform finite temperature simulations of SU(2) lattice gauge fields in two spatial dimensions. We calculate the correlation length and find that it appears to diverge at a critical temperature, indicating a second order phase transition. Our average value for the associated critical exponent is gamma = 0.975(-0.035)+0.045 which is consistent with the value gamma = 1 in the D = 2 Ising model. We calculate the critical temperature, T(c), in units of the string tension, sigma, and extrapolate 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 obtain 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.