Aperiodic magnetic models on the Wheatstone hierarchical lattice

Abstract

Aperiodic Ising models on Wheatstone hierarchical lattices, induced by two-letter substitution sequences, are analyzed within a transfer matrix framework. The numerical iteration of the set of maps leads to values for the thermodynamical properties as functions of the temperature, from which the critical properties are evaluated. Relevant geometric fluctuations in the distribution of bonds induced by substitution rules play an essential role for the occurrence of changes in the critical behavior of the aperiodic model in comparison with its homogeneous counterpart. We have found both irrelevant and relevant fluctuations already for the first two members of this family. Results are important to the understanding of the behavior of aperiodic Ising model on planar lattices. © 2005 Elsevier B.V. All rights reserved.