The variational principles introduced by Kadanoff et al. in the renormalization theory are analyzed. It is shown that the values for the specific heat critical exponent α which can be found by a variational method are restricted to α 0 or α = 1 (first order transition). The reason is the...

We report several studies of cross-over behavior in Anderson localization for weak magnetic fields (B) and near two dimensions. Background-field methods are employed and extended for renormalization group purposes. The results are consistent with the theory for strong B and with the weak...

The variational principle is presented for a continuous renormalization transformation. It is shown that a strict application of the variational method leads to a singularity in the variational parameter which is related to that in the free energy. The equations governing the behaviour of the...

The Kadanoff lowerbound renormalization transformation when applied to the 2-dimensional q-state Potts model, is found to show a bifurcation phenomenon at q = 4, that might be considered as signalling the onset to the first-order transition. At the value of the free parameter where the...

Some of the two dimensional statistical mechanical models likely to be discussed in this meeting are described and their properties outlined. The phase transitions of most of the models can be discussed as lying upon lines of continuously varying critical behavior. One particularly simple...

A simplified model of reptation is presented. The Master Equation of the model is systematically solved by expansion in powers of the strength of the driving field. From the explicit form of the probability distribution, exact conclusions can be drawn about the average shape of the polymer, its...

A fluid interface near a critical point is commonly pictured as an intrinsic interface broadened by thermally excited capillary waves. A comparison of the capillary-wave theory with experiments is hampered by the presence of two short-wavelength cutoff parameters in the theory. We review a...

Critical singularities disappear in systems placed in an inhomogeneous field that couples with the order parameter. On the basis of simple renormalization arguments we show that the change from singular behavior in the absence of a field to nonsingular behavior in the presence of a field is...

The paper deals with the question how critical fluctuations in gases are affected by the presence of a gravitational field. We have investigated the effects of gravity using a squared-gradient approximation for the free energy density. It is found that the order-parameter correlation function...

The influence of gravity on the suppression of the capillary fluctuations of a liquid-vapour interface is studied by simulating a Lennard-Jones system in two dimensions in a gravity like field. The results are compared to the capillary wave theory. A lower length cut-off is found for the...