Peter Young's Home Page
Abstract
The recently proposed state of a disordered
type-II superconductor in a magnetic
field, the ``vortex glass'', is discussed and compared with the ``spin
glass'' transition in magnetic systems. We discuss the results of
Monte Carlo simulations
on a model that seems to have the necessary ingredients to
describe this state, in two, three and four dimensions.
The technique involves
computing the free energy cost to twist the direction of the phase of the
condensate and analyze the results by finite-size scaling. The results
show clearly that the model has
different behavior in the different dimensions: $d=4$
clearly has a finite transition temperature; $T_c$, $d = 3$ is close to the
marginal dimension (though $T_c$ is probably also finite); and $d=2$ only
has a transition at $T=0$. The results are compared with experiments.
Recent ideas on obtaining transport properties, such as current-voltage
characteristics, from Monte Carlo simulations are also discussed. It is
shown that the fluctuation-dissipation theorem and the Kubo formula,
familiar from continuous-time Hamiltonian dynamics, are also valid for
discrete-time stochastic Monte Carlo dynamics.
Physics Home Page