Stable and runaway bubble merger in a model for Rayleigh-Taylor unstable interfaces

A statistical model for the growth of bubbles in a Rayleigh-Taylor unstable interface is analyzed. Runaway and uniform growth regimes are observed. Starting from a random configuration, in which neighboring bubbles are uncorrelated, runaway is found to be the expected initial transient with velocities and accelerations growing exponentially. However neighboring bubble correlations develop dynamically, which may lead to a self-limiting regime of uniform growth and constant acceleration. The observed constant acceleration rate is non-universal.     

Real-space renormalization group investigation of the three-dimensional semi-infinite mixed spin ising model

Within a real-space renormalization group framework we study the three-dimensional semi-infinite mixed spin Ising model (spins =1/2 andS=1). The bilinear (K _s ) and the biquadratic (L _S ) interactions on the surface might be different from the bulk onesK _B andL _B . The parameter space is four dimensional. We find 26 fixed points describing a large variety of critical behaviour. The effect ofL _B andL _S on the surface transition is investigated.Supported by the agreement of cooperation between the DFGW. Germany and the CNR-Maroc     

A renormalization group model with non-Gaussian fixed point

We apply short distance scaling to the Wick square of a massive free time zero field and show that the characteristic functionals of the suitably renormalized fields have a short distance limit. The properties of the limiting characteristic functionals allow us to find a class of the other renormalization group invariant processes. They are all non-Gaussian, but can be expressed by superposition of the Gaussians. We also discuss the test function spaces and the pointwise limit of the n-point functions.     

Migdal-Kadanoff renormalization group for theO(n) model

We perform a Migdal-Kadanoff renormalization group calculation on anO(n) symmetric model on ad-dimensional hypercubic lattice,d=2, 3. We find that in two dimensions the critical fixed point disappears asn=n _KT1.96, which is in good agreement with the exact valuen _KT=2. In three dimensions the fixed point persists much longer, albeit not all the way up to infinity. Surface critical phenomena in a semiinfiniteO(n) model are also considered.     

On-shell renormalization for particles with mixing

The subject of our discussion are the on mass-shell renormalization conditions in any order of the perturbative calculations with particle mixing. The imaginary parts of the propagators which are connected with the particle decay width are taken into account. The phenomenological LSZ relation for unstable particles is discussed. The on-shell renormalization condition for the mixing of particles with spins 0+0, 0+1. and 1+1 is presented.     

The classical Ising model: A quantum renormalization group approach

Proceeding from the equivalence between the d-dimentional classical Ising model and the (d?1)-dimentional quantum mechanical Ising model in a transverse magnetic field, we study the critical properties of the classical model via the quantum mechanical model. Quantum renormalization group transformations based on the truncation method and the ground state projection operator method are used to calculate the critical exponents. They are found to agree well with the “exact” values.     

Real space renormalization group investigation of three-dimensional Ising spin glasses

Using real space renormalization group techniques we determine the phase diagram of bond dilute frustrated nearest-neighbor Ising three-dimensional simple cubic (sc) and body-centered cubic (bcc) systems.     

Mean-field renormalization group with reaction field for diluted ising model

Summary A mean-field renormalization group method including the reaction field is applied to diluted Ising systems. Two-dimensional bond dilution and both two- and three-dimensional site dilution are considered. For low and intermediate dilution, the phase diagrams agree well with other predictions, while for large dilution (near the percolation threshold) pathologies may show up related to the choice of the reaction field at low temperature.

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Riassunto Un metodo di rinormalizzazione basato sul campo medio con correzioni di campo di reazione è applicato a modelli di Ising diluiti. Sone trattati sia il caso di legami diluiti in due dimensioni, che quello di siti diluiti in due e tre dimensioni. Per diluizioni non troppo elevate il diagramma delle fasi è in buon accordo con altre predizioni. Ad alte diluizioni (vicino alla soglia di percolazione) possono verificarsi patologie dovute all’inadeguatezza del campo di reazione a basse temperature.

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Резюме Группа перенормировки для среднего поля, включая поле взаимодействия, применяется к системам Изинга. Рассматриваются двумерное разбавление связи и двумерное и трехмерное разбавление узлов. Для слабого и среднего разбавления фазовые диаграммы хорошо согласуются с другими предсказаниями, однако для сильного раэбавления (вблизи порога перколяции) могут возникать патологии, связанные с выбором взаимодейстния при низкой температуре.

     

Fixed points of renormalization group for the hierarchical fermionic model

A fermionic version of Dyson's hierarchical model is defined. An exact renormalization group transformation is given as a rational transformation of two-dimensional parameter space. Two branches of nontrivial fixed points are described, one of which bifurcates from the trivial Gaussian branch. The existence of the thermodynamic limit for these branches of fixed points is investigated.     

Two-loop renormalization group equations in the standard model

Two-loop renormalization group equations in the standard model are recalculated. A new coefficient is found in the beta function of the quartic coupling and a class of gauge invariants is found to be absent in the beta functions of hadronic Yukawa couplings. The two-loop beta function of the Higgs mass parameter is presented in complete form.     

A renormalization group with periodic behaviour

An explicit example of a renormalization group with periodic behaviour is constructed and analyzed using both truncated recurrence relations and direct numerical computations. This renormalization procedure arises in the context of transition to turbulence.     

Equivalence of model space techniques and the renormalization group for a separable model problem

Lee–Suzuki similarity transformations and Krenciglowa–Kuo folded diagrams are two common methods used to derive energy independent model space effective interactions for nuclear many-body systems. We demonstrate that these two methods are equivalent to a Renormalization Group (RG) analysis of a well-studied problem in quantum mechanics. The effective low-momentum potentials V_eff obtained from model space methods are shown to obey the same scaling equation for V_eff that RG arguments predict. This indicates that model space methods might be of interest to those studying low-energy nuclear physics using Effective Field Theories (EFT). We find the new result that all of the different energy independent model space techniques yield a unique low-momentum V_eff when applied to the toy model under consideration.     

Real space renormalization group theory of the percolation model

A cluster expansion renormalization group method in real space is-developed to determine the critical properties of the percolation model. In contrast to previous renormalization group approaches, this method considers the cluster size distribution (free energy) rather than the site or bond probability distribution (coupling constants) and satisfies the basic renormalization group requirement of free energy conservation. In the construction of the renormalization group transformation, new couplings are generated which alter the topological structure of the clusters and which must be introduced in the original system. Predicted values of the critical exponents appear to converge to presumed exact values as higher orders in the expansion are considered. The method can in principle be extended to different lattice structures, as well as to different dimensions of space.This paper is dedicated to Prof. Philippe Choquard.     

Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

Block renormalization group for Euclidean Fermions

Block renormalization group transformations (RGT) for lattice and continuum Euclidean Fermions in d dimensions are developed using Fermionic integrals with exponential and -function weight functions. For the free field the sequence of actionsD _k generated by the RGT from D, the Dirac operator, are shown to have exponential decay; uniform ink, after rescaling to the unit lattice. It is shown that the two-point functionD ^–1 admits a simple telescopic sum decomposition into fluctuation two-point functions which for the exponential weight RGT have exponential decay. Contrary to RG intuition the sequence of rescaled actions corresponding to the -function RGT do not have uniform exponential decay and we give examples of initial actions in one dimension where this phenomena occurs for the exponenential weight RGT also.