No abstract

We calculate the static critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by the renormalization group method within the minimal subtraction scheme in two-loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability border lines in the space of the order parameter components n_|| and n_perpendicular and spatial dimension d are calculated. The essential features obtained already in two-loop order for the interesting case of an antiferromagnet in a magnetic field ( n_|| =1, n_perpendicular =2 ) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points, leading to very small transient exponents. We are also able to calculate the flow of static couplings, which allows us to consider the attraction region. Depending on the nonuniversal background parameters, the existence of different multicritical behavior (bicritical or tetracritical) is possible, including a triple point.

We analyze the field theoretic functions of the dynamical model C in two-loop order. Our results correct long-standing errors in these functions published by several authors. We discuss, in particular, the fixed points for the ratio w* of the two time scales involved, as well as their stability. The regions of the "phase diagram," whose axes are the spatial dimension d and number of order parameter components n, correspond to these fixed points; previous authors have found, in addition, an anomalous region in which the scaling properties were unclear. We show that such an anomalous region does not exist. There are only two regions: one with a finite fixed-point w* where the dynamical exponent z=2+alpha/nu, and another where w*=0 and z is equal to the model A value. We show how the one-loop result is recovered from the two-loop result in the limit epsilon=4-d going to zero.

We derive the nonasymptotic expressions for the frequency-and temperature-dependent sound velocity and sound absorption near a critical point in a mixture within renormalization group theory in one-loop order. The dynamic model considered is an extension of the corresponding model for pure fluids including concentration fluctuations. The theoretical result for the complex sound velocity is the same as at consolute points and gas-liquid critical points reflecting universality. Differences observed in the experiments at the two critical points mentioned are due to the different behavior of the sound velocity at T c , which is finite in mixtures and zero in pure fluids, as well as due to nonasymptotic effects. Near the consolute point we compare our result with the phenomenological theory of Ferrell and Bhattacharjee ͓Phys. Rev. B 24, 4095 ͑1981͒; Phys. Rev. A 31, 1788 ͑1985͔͒ and near the gas-liquid critical point with experiments in the 3 He-4 He mixture. A genuine dynamic parameter not considered so far and related to the critical enhancement of the thermal conductivity appears in the nonasymptotic expressions of the transport coefficients and the complex sound velocity. All nonuniversal background parameters of the complex sound velocity are fixed by a comparison of the corresponding theoretical expressions for the transport coefficients with experiments.

No abstract