Vortices and the Ginzburg-Landau phase transition

The methods for studying the role of vortex loops in the phase transition o f the Ginzburg-Landau theory of superconductivity using lattice Monte Carlo simulations are discussed. Gauge-invariant observables that measure the pr operties of the vortex loop distribution are defined. The exact relations b etween the lattice and continuum quantities make it possible to extrapolate the results of the simulations to the continuum limit. The relationship be tween spontaneous symmetry breaking and phase transitions is also reviewed, with an emphasis on the fact that a local symmetry cannot be broken. (C) 1 998 Elsevier Science B.V. All rights reserved.