1303.3829 (F. Antenucci et al.)

Renormalization Group on hierarchical lattices in finite dimensional
disordered Ising and Blume-Emery-Griffiths Models    [PDF]

F. Antenucci, A. Crisanti, L. Leuzzi

Renormalization group analysis on hierarchical lattices is a valuable tool to understand the critical behavior of statistical mechanical models. In presence of quenched disorder, where position space renormalization group procedures are still on their way, it has the advantage to be analytically applicable. In some model cases, though, predictions obtained with the Migdal-Kadanoff bond removal approach fail to qualitatively reproduce critical properties obtained in mean-field approximation or by numerical simulations. We focus on the critical behavior of Ising and Blume-Emery-Griffiths models on hierarchical lattices microscopically more similar to finite dimensional Bravais lattices than those belonging to the Migdal-Kadanoff class in order to understand if and how different behaviors are associated with hierarchization.

View original: http://arxiv.org/abs/1303.3829