Functional Renormalization Group Method Applied to Long Range Minimal Models

N. Dupuis, Léonie Canet, Astrid Eichhorn +4 more

D.V. Shapoval, M. Dudka

We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance x as ∼ x - d - σ in a d-dimensional space. It is known to belong to a new long-range random universality class for certain values of the decay parameter σ. Exploiting the field-theoretic renormalization group approach within the minimal subtraction scheme, we compute the three-loop renormalization group functions. On their basis, with the help of asymptotic series resummation methods, we estimate the correlation length critical exponent ν characterising the new universality class for d = 3 and for those values of σ for which long-range interactions are relevant for the critical behaviour.

Masashi Kojo, Kikuji Hirose

Abstract We derive a practical algorithm to study many‐electron systems based on the path‐integral renormalization group (PIRG) method within the framework of the real‐space finite‐difference (RSFD) approach. The PIRG method, originally developed for investigating strongly correlated electron systems, has been successfully applied to some models such as Hubbard models. However, to apply this method to more realistic systems of electrons with long‐range Coulomb interactions in the RSFD approach, the one‐body Green's function, which requires large computational resources, must be removed. For the same reason, an efficient algorithm for computing the Fock matrix is needed. The newly proposed algorithm is free of the one‐body Green's function and enables us to compute the Fock matrix efficiently. Our result shows a significant reduction in CPU time and the possibility of using the present algorithm as a practical numerical tool. Copyright © 2008 John Wiley & Sons, Ltd.

Roberto Percacci A

Andreas Wipf

A. Langari, Vahid Karimipour

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the xxz spin 1/2 Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin-spin correlation function which confirms the absence of long-range order in the massless region of the 1D xxz model.