DENSITY CORRELATION-FUNCTION AND DYNAMIC TRANSIENT EXPONENTS FOR LIQUID-HELIUM AT AND ABOVE T-LAMBDA

The critical dynamics of liquid helium are studied by means of renormalized field theory on the basis of the symmetric planar-spin model of Halperin, Hohenberg, and Siggia. The stability problem of the dynamic fixed point is discussed in detail. Two-loop results suggest, but do not establish, the stability of the dynamic scaling fixed point. The previously found small fixed point value w*~O(0.15) is tentatively confirmed which implies a small ratio of relaxation rates of the order parameter and the entropy. The ensuing dynamic transient exponents are calculated. The density correlation function is determined to O(ε=4-d) at and above Tλ. Its properties in the case w*≪1 provide quantitative support for the recently proposed explanation of the discrepancy between theory and light scattering experiments. A small value of w* implies pronounced peaks of the frequency spectrum at finite frequencies at and above Tλ. It also suppresses the temperature dependence of finite-frequency properties over an enlarged critical region as found in light scattering measurements. The quantitative relation between the value of w*>0 and observable properties of the frequency spectrum is computed. © 1979 Springer-Verlag.