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.     

A one-loop renormalization group analysis of the Gelmini-Roncadelli model

A one-loop renormalization group analysis is presented of the Gelmini-Roncadelli model of neutrino mass generation via an extended Higgs sector. We are unable to find values for the quartic scalar couplings at the W mass scale which cause the combined Higgs-gauge couplings to evolve to a stable fixed point of the renormalization group. As a consequuence this model may well be “trivial” in the same sense as λφ⁴ theory is believed to be in four dimensions.     

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.     

Mean-field renormalization group for the q-state clock spin-glass model

The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method.     

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.     

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.     

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.     

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.     

A new proposal for the determination of the renormalization group trajectories by the Monte Carlo renormalization group method

We present a new method for calculating block renormalized couplings by Monte Carlo renormalization group. This method has several advantages with respect to the existing ones and can be applied for any value of the coupling constants. A preliminary numerical study of the 2-dimensional O(3) non linear σ-model is also presented.     

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.