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Springer proceedings in physics

Numerical Study of Critical Exponents for Kosterlitz-Thouless Transition Systems

Yukiyasu Ozeki, Nobuyasu Ito

Published Jan 1, 2004• 4 citations
Publisher
DOI
10.1007/978-3-642-59293-5_15

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The critical exponents are estimated for the gauge glass model in two dimensions, in which only the Kosterlitz-Thouless (KT) phase appears in the low-temperature regime. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents: the static exponent η and the dynamical exponent z. Since the system exhibits criticality in the whole KT phase, we estimate the exponents on the boundary as well as inside the KT phase. The static exponent η depends on both the temperature and the strength of randomness, while the dynamical one z is almost constant throughout the KT phase, including the boundary.
Using analytical and discretized Migdal-Kadanoff renormalization-group methods it is shown that similar to the standard XY model the two-component uniform multipolar systems undergo a Kosterlitz-Thouless transition in two dimensions. The critical behavior of the multipole-multipole correlation function is governed by a set of critical exponents that depend on the rank t of multipole moments. At the Kosterlitz-Thouless transition they become universal for all systems. An exactly renormalizable multipolar model is introduced. The behavior of this model on fractal and hierarchical lattices is studied. The T=0 scaling exponent of the two-component multipolar systems on a Sierpinski carpet is shown to be negative, so no Kosterlitz-Thouless transition can be expected to take place in this case.