Renormalization group approach to the one-dimensional hubbard model

An approximate decimation method is applied to the one-dimensional half-filled Hubbard model. The specific heat, the entropy and the magnitude of local moments are calculated. The results are in good agreement with those obtained by Shiba at high temperatures.     

Renormalization group for a critical lattice model

New methods are developed for the study of the Kadanoff-Wilson renormalization group for critical lattice systems of unbounded spins. The methods are based on a combination of expansion and analyticity techniques and are applied to a nonlocal hierarchical model of the dipole gas. They remove the main obstacle against the use of the block spin strategy in more realistic models such as φ _d ^/4 , the dipole gas and the anharmonic crystal.     

Renormalization group study of a critical lattice model

We start a nonperturbative study of the Wilson-Kadanoff renormalization group (RG) in weakly coupled massless lattice models. Nonlocal hierarchical models are introduced to mimic the infrared behaviour of the \(\tfrac{1}{2}(\nabla \phi )^2 + \lambda (\nabla \phi )^4\) model and the like. The RG is shown to drive these to the line of fixed points corresponding to the massless \(\tfrac{1}{2}c_\infty (\lambda )(\nabla \phi )^2\) models.     

Renormalization group approach to a p-wave superconducting model

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.     

Critical surface of the quenched bond-diluted cubic model in self-dual lattice: Renormalization group approach

Summary We propose a quite simple real-space renormalization group, which enables us to calculate (for the first time, as far as we know, and presumably with high precision) the critical surface of the quenched bond-diluted discreteN-vector ferromagnet in a self-dual lattice.     

Renormalization group study of anomalous acoustic behavior in critical percolation network

We study the acoustic behavior of critical percolation network within a real-space renormalization group framework recently proposed by Ohtsuki and Keyes. Using large cell Monte Carlo renormalization group calculations, we obtain the exponent for anomalous sound dispersion K ^1+x/v . Our estimate 2x/v0.80 is in agreement with the exponent for anomalous diffusion in percolation clusters =(–)/v.     

Renormalization group approach to exact sampling

In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson's "coupling from the past" approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the Markov chain Monte Carlo dynamics from parts of the configurations (patches) on increasing length scales, and it allows us to generate "exact samples" of the Boltzmann distribution, which are rigorously proven to be uncorrelated with the initial condition. We validate our approach in the two-dimensional Ising spin glass on lattices of size 64 x 64.     

Renormalization group approach to chemical instabilities

The effects of inhomogeneous fluctuations on instabilities in non linear chemical models are studied using renormalization group techniques. The onset of non classical behaviour is discussed.Chercheur Qualifié du Fonds National de la Recherche Scientifique     

Renormalization group approach to Sterman-Weinberg jets

A renormalization group approach is developed for single-jet Sterman-Weinberg cross sections. For small δ², but large Q²δ², the complete δ², Q² and ? dependence of the cross section for e⁺e^? annihilation is shown to be calculable in QCD systematically in powers of α(Q²). ? is not assumed to be small.     

Renormalization group approach to spin glass systems

A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining transformation, that is performed on the overlap probability measure. Universality classes are thus naturally defined on a large set of models, going from and Gaussian spin glasses to Ising and fully frustrated models, and others. The proposed analysis is tested numerically on the Edwards-Anderson model in d = 4. Good estimates of the critical index ν and of T _c are obtained, and an RG flow diagram is sketched for the first time. Received 17 November 2000     

Renormalization group approach to QCD phase transitions

Effective scalar theories for QCD are proposed to investigate the deconfining and chiral phase transitions. The orders of the phase transitions are determined by infrared stabilities of the fixed points. It is found that the transitions inSU (3) gauge theories are of 1st order for any number of massless flavors. The cases ofSU (2) andSU (4) gauge theories are also discussed.     

Renormalization group approach to the spin-1 Bose gas

A field theoretical renormalization group approach at two loop level is applied to the homogeneous spin-1 Bose gas in order to investigate the order of the phase transition. The beta function of the system with d=4-epsilon dimensions is determined up to the third power of the coupling constants and the system's free energy on the border of the classical stability is given in next to leading order. It is found that the phase transition of the interacting spin-1 Bose gases with weak spin-dependent coupling constant values is of first order.     

Phases coexistence and surface tensions for the potts model

Theq states Potts model exhibits a first order phase transition at some inverse temperature β _t between “ordered” and “disordered” phases forq large as proved in [1]. In space dimension 2 we use theduality transformation as aninternal symmetry of the partition function at β _t to derive an estimate on the probability of a contour. This enables us to prove the preceding result and the following new results:

1. The discontinuity of the mass gap at β _t .
2. The existence of astrictly positive surface tension between two ordered phases up to β _t .
3. The existence of a non-zero surface tension between an “ordered” and the “disordered” phase at β _t .

     

Renormalization group approach to lattice gauge field theories

We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized effective actions by cluster expansions in one step renormalization transformations. We construct also -functions and we define a coupling constant renormalization by a recursive system of renormalization group equations.     

Renormalization group approach to lattice gauge field theories

The fluctuation field integral, constructed in Part I, is represented by the exponentiated cluster expansion. It is proved that the terms of the expansion satisfy the inductive assumptions. This completes the construction of the sequence of effective actions in the small field approximation.Work supported in part by the Air Force under Grant AFOSR-86-0229 and by the National Science Foundation under Grant DMS-86-02207