2 PHASES OF THE ANYON GAS AND BROKEN TAU-SYMMETRY - SOME EXACT RESULTS

We report the first exact finite-temperature studies of anyons. Our method is an extension to finite T of earlier numerical work with small numbers of anyons on a lattice. We study the spontaneous magnetization M0(T), since this signature has been identified as a key signature of broken T symmetry for anyon models. Our results confirm the two-phase picture suggested by earlier work: we find a low-temperature regime where M0 is very small or zero, and a high-temperature regime where M0 is of O(0.1-mu-B) per particle. In the high-temperature regime we can obtain an excellent estimate of M0(T) in the thermodynamic limit (which we will call M0 infinity), since our finite-size results extrapolate smoothly with little scatter. Our values for M0 infinity can then be compared with the results of mu-SR experiments on high-temperature superconductors, which set an upper experimental bound on the internal fields from such moments. We find that M0 infinity in a bulk material of many planes will almost certainly give a signal well above this threshold if (and only if) the planes are ordered ferromagnetically. In the antiferromagnetic case (which is strongly favored energetically) the signal from M0 infinity is probably undetectable. Finally, we estimate the transition temperature T(c) from our finite-size studies, obtaining a value on the order of a few hundred Kelvins.