Renormalization Group Approach to Interacting Crumpled Surfaces: the Hierarchical Recursion *
نویسندگان
چکیده
We study the scaling limit of a model of a tethered crumpled D-dimensional random surface interacting through an exclusion condition with a fixed impurity in d-dimensional Euclidean space by the methods of Wilson's renormalization group. In this paper we consider a hierarchical version of the model and we prove rigorously the existence of the scaling limit and convergence to a non-Gaussian fixed point for 1 ≤ D < 2 and ǫ > 0 sufficiently small, where ǫ = D − (2 − D) d 2 .
منابع مشابه
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...
متن کاملRenormalization of crumpled manifolds.
We consider a model of D-dimensional tethered manifold interacting by excluded volume in IR with a single point. By use of intrinsic distance geometry, we first provide a rigorous definition of the analytic continuation of its perturbative expansion for arbitrary D, 0< D < 2. We then construct explicitly a renormalization operation R, ensuring renormalizability to all orders. This is the first ...
متن کاملGlobal Aspects of the Renormalization Group Flows of Dyson’s Hierarchical Model
Dyson’s hierarchical model (HM) is a lattice scalar model for which the effective potential can be calculated very accurately using the renormalization group method. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigorous and numerical result...
متن کاملA NUMERICAL RENORMALIZATION GROUP APPROACH FOR AN ELECTRON-PHONON INTERACTION
A finite chain calculation in terms of Hubbard X-operators is explored by setting up a vibronic Harniltonian. The model conveniently transformed into a form so that in the case of strong coupling a numerical renormalization group approach is applicable. To test the technique, a one particle Green function is calculated for the model Harniltonian
متن کاملA numerical renormalization group approach for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators
Theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. Since in this study a Two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thisHamiltonian...
متن کامل