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, v=O. 36963. . . , but also gives a criterion for its own range of validity amounting to t « 10,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 g+ » 10'3 lattice spacings. The implications of these results for experimental verification are discussed.

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The methodology described and utilized previously by the author, involving the use of nonequilibrium thermodynamics in the analysis of the spectrum of light scattered quasielastically by crystals, is applied to piezoelectric crystals. An additional thermodynamic variable, the electric polarization, is taken into account and assumed to be a relaxing variable, Solution of the resulting equations in the case of KH, PO4 leads, as expected, to the appearance of a polarization relaxation line in the spectrum. The spectrum is calculated for several values of the two relevant parameters: the polarization relaxation frequency and the ratio of C« isothermal elastic constants at constant electric field and constant polarization. For a fixed polarization-relaxation frequency, it is found that as the ratio of elastic constants decreases (the characteristic behavior as the ferroelectric phase transition in KH, PO4 is approached), the intensity of the relaxation line increases at the expense of the Brillouin lines, In contrast with standard treatments of coupled modes in piezoelectric crystals, no adjustable parameters are involved in determining the spectrum. I. INTROI3UCTION In previous work by the same author' (hereafter referred to as I) a description was given and illustrate examples provided of the utilization of nonequilibxium thermodynamics (NETD) in the determination of quasielastic light scattering spectra of crystals. The methodology is summarized in

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