Real Space Renormalization Techniques

Mohamad Al Hajj, Nathalie Guihéry, Jean Paul Malrieu

Theodore W. Burkhardt, J. M. J. van Leeuwen

O Gittsovich, R Hübener, E Rico +1 more

In this paper, we introduce a real-space renormalization transformation for random spin systems on two-dimensional (2D) lattices. The general method is formulated for random systems and results by merging two well-known real-space renormalization techniques, namely the strong disorder renormalization technique and the contractor renormalization technique. We analyze the performance of the method on the 2D random transverse field Ising model.

Leszek Samson, G. Spronken, M. Avignon

Sarker's real-space renormalization-group method, applied previously to the one-dimensional dimerized XY model, is used to study the one-dimensional pure and dimerized Heisenberg models. Comparison of critical exponents (the dynamical and the gap exponents) with exact or conjectured values indicates that the method, in its original version, does not yield an improved real-space technique, at least for the models studied for which the opening of the gap leads to essential singularity or logarithmic corrections.

Patricio Cordero A