Wegner expansion

Extension of the classical Landau-Ginzburg expansion to incorporate nonclassical critical fluctuations and to yield detailed crossover functions were first presented by Nicoll and coworkers [313, 314] and later extended by Chen et al. [315, 316]. These extensions match Ginzburg theory to RG theory, and thus interpolate between the lower-order terms of the Wegner expansion at T -C Afa and mean-field behavior at f Nci-... 

The exponent )8 and the amplitudes B, can be found by a least square analysis. The data for cesium, rubidium, and mercuiy can be fitted within their experimental uncertainty to the Wegner expansion, Eq. (6.3). The values obtained for are consistent with the best renormalization group calculations. The analysis is consistent with the observations made for other fluids in that the exponent approaches the theoretical value... 

According to the Wegner expansion,[12] the measured coexistence curves were analyzed by the expressions... 

In 1972 Wegner [25] derived a power-series expansion for the free energy of a spin system represented by a Flamiltonian roughly equivalent to the scaled equation (A2.5.28). and from this he obtained power-series expansions of various themiodynamic quantities around the critical point. For example the compressibility... 

There are other scenarios for an apparent mean-field criticality [15, 17]. The most likely one is crossover from asymptotic Ising behavior to mean-field behavior far from the critical point, where the critical fluctuations must vanish. For the vicinity of the critical point, Wegner [43] worked out an expansion for nonasymptotic corrections to scaling of the general form... 

Expansion of the asymptotic power law for the order parameter in terms of a Wegner series (3) leads to [43]... 

Analysis of the critical behavior of thermodynamic properties is complicated by the fact that simple asymptotic-power law behavior is restricted to temperatures very close to the critical point. Investigations of metals in this range are limited by the severe experimental difficulties. It is necessary, therefore, to consider not only the asymptotic critical behavior, but also the corrections needed to analyze the experimental data over a larger range. Wegner (1972) worked out an asymptotic series expansion for critical behavior. The translation of Wegner s expansion into the terminology of fluids shows that measured properties should obey modified power laws of the form... 

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