The Vortex Glass

Lecture at the Ray Orbach Inaugural Symposium on "Random Magnetism and High_Temperature Superconductivity" Riverside, California, March 1993.
A.P. Young
Edited by W.P. Beyerman. N.L. Huang-Liu and D.E. MacLaughlin, Published by World Scientific (1994).

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.

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