Field behavior of an Ising model with aperiodic interactions

Details Field behavior of an Ising model with aperiodic interactions Field behavior of an Ising model with aperiodic interactions

2000-05-02

arxiv.org/abs/cond-mat/0005061v1

Int. J. Mod. Phys. B 14, 1473 (2000)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1142/S0217979200001461

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.

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