Field behavior of an Ising model with aperiodic interactions

Abstract

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal-Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.

9 pages, 1 figure (included). Accepted for publication in Int. J. Mod. Phys. B

References in corpus (2)

• Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions
• Critical behavior of an Ising model with aperiodic interactions