The calculation of critical amplitudes in SU(2) lattice gauge theory
We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of (3 + 1)-dimensional SU(2) gauge theory. To this end we study the corrections due to irrelevant exponents in the scaling functions. As a guiding line for determining the critical amplitudes we use envelope equations which we derive from the finite site scaling formulae of the observables. We have produced new high precision data on N-sigma(3) x 4 lattices for N-sigma = 12, 18, 26 and 36, With these data we find different corrections to the asymptotic scaling behaviour above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C+/C- = 4.72(11) and thus in excellent agreement with a recent measurement for the 3d Ising model. (C) 1999 Published by Elsevier Science B.V.
Critical exponents of the N-vector model
Recently the series for two renormalization group functions (corresponding to the anomalous dimensions of the fields and ) of the three-dimensional field theory have been extended to next order (seven loops) by Murray and Nickel. We examine the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within the errors of the previous evaluation. Exponents such as (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou-Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published expansions (order ), we have also re-analysed the determination of exponents from the -expansion. The conclusion is that the general agreement between -expansion and three-dimensional series has improved with respect to Le Guillou-Zinn-Justin.
Second sound very near Tλ
The results of an experimental investigation of the evolution of planar, non-linear, second-sound pulses in superfluid4He, to within 650 nK of the λ-transition, are presented. A new method for extracting the second-sound velocity and damping is demonstrated. As predicted from two-fluid hydrodynamics, the pulses are well modeled by the solutions of Burgers' equation. The second-sound velocity (u20) and damping (D2) are extracted from fits of the model to the data. Damping data are obtained in this fashion to 3×10−7 in reduced temperature at saturated vapor pressure; nearly two decades closer to Tλ then any previous measurements. The superfluid density is extracted from theu20 measurements and the critical exponent, ζ, is determined. A study of very large amplitude pulses near Tλ is also presented. These pulses extend well beyond the range of validity of Burgers' equation. The amplitude of the shock that forms at the trailing edge of the pulse is observed to saturate as a function of heater power and then decrease suddenly, as has been previously observed away from Tλ. However, the pulse shapes are quite different from any previously observed.