Dislocations and melting in two dimensions: The critical region

Abstract

A new analysis is presented of the critical-point behavior of two-dimensional melting in the Kosterlitz-Thouless-Nelson-Halperin-Young theory. The analysis confirms the Kosterlitz-Thouless-Nelson-Halperin-Young critical-point exponent, ν̅=0.36963…, but also gives a criterion for its own range of validity amounting to t<<10^-3, where t is the reduced temperature. Both results are confirmed by direct numerical computation, and it is shown that the corresponding range of correlation lengths is ξ+>>10^13 lattice spacings. The implications of these results for experimental verification are discussed.