Phenomenological renormalization group methods

Phenomenological Renormalization Group Methods

Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate critical behavior of the model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this wo...

On a development of the phenomenological renormalization group

We propose a modification of the Nightingale renormalization group for lattice spin and gauge models by combining it with the cluster decimation approximation. Essential ingredients of our approach are: 1) exact calculation of the partition and correlation function on a finite lattice strip; 2) preservation of the mass gap or the second moment correlation length, computed in the infinite strip ...

Renormalization Group Renormalization Group

Renormalization group methods for nonlinear parabolic equations

Renormalization group (RG) methods are described for determining the key exponents related to the decay of solutions to nonlinear parabolic differential equations. Higher order (in the small coefficient of the nonlinearity) methods are developed. Exact solutions and theorems in some special cases confirm the RG results.

Time-Dependent Real-Space Renormalization Group Method

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...