Classical Phase Fluctuations in High Temperature Superconductors

Phase fluctuations of the superconducting order parameter play a larger role in the cuprates than in conventional BCS superconductors because of the low superfluid density ${\rho }_s$ of a doped insulator. In this paper, we analyze an $\mathrm{XY}$ model of classical phase fluctuations in the high temperature superconductors using a low temperature expansion and Monte Carlo simulations. In agreement with experiment, the value of ${\rho }_s$ at temperature $T=0\mathrm{}$ is a quite robust predictor of $T_c$, and the evolution of ${\rho }_s$ with $T$, including its $T$-linear behavior at low temperature, is insensitive to microscopic details.