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, $\overline{\nu }=0.36963\mathrm{}\dots$, but also gives a criterion for its own range of validity amounting to $t<<{10}^{-3\mathrm{}}$, 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 ${\xi }_{+}>>{10}^{13}$ lattice spacings. The implications of these results for experimental verification are discussed.