Solving the Ginzburg-Landau equations by simulated annealing

Abstract

We propose and demonstrate the power of a novel approach to the solution of the Ginzburg-Landau equation based on minimizing the free-energy functional with the numerical technique of simulated annealing instead of minimizing it analytically and then solving the resulting nonlinear partial differential equations. We present calculations of the magnetization versus magnetic field that agree well with the predictions of Abrikosov and others for a homogeneous, isotropic type-II superconductor near ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$. We also summarize the extension of the method to the calculation of the properties of an inhomogeneous, anisotropic superconductor.