Critical properties of an aperiodic model for interacting polymers

TL;DR

This paper explores how aperiodic interactions influence the critical behavior of an interacting two-polymer model on hierarchical lattices, revealing new universality classes and attractors through renormalization-group and transfer-matrix methods.

Contribution

It introduces a detailed analysis of aperiodic effects on polymer criticality, identifying novel attractors and universality classes via exact renormalization-group and thermodynamic calculations.

Findings

Aperiodic interactions can destabilize the uniform critical fixed point.

New attractors, such as two-cycles and closed curves, emerge due to relevant geometric fluctuations.

The model suggests the existence of a new critical universality class.

Abstract

We investigate the effects of aperiodic interactions on the critical behavior of an interacting two-polymer model on hierarchical lattices (equivalent to the Migadal-Kadanoff approximation for the model on Bravais lattices), via renormalization-group and tranfer-matrix calculations. The exact renormalization-group recursion relations always present a symmetric fixed point, associated with the critical behavior of the underlying uniform model. If the aperiodic interactions, defined by s ubstitution rules, lead to relevant geometric fluctuations, this fixed point becomes fully unstable, giving rise to novel attractors of different nature. We present an explicit example in which this new attractor is a two-cycle, with critical indices different from the uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we find a surprising closed curve whose points are attractors of period two, associated with a marginal operator. Nevertheless, a scaling analysis indicates that this attractor may lead to a new critical universality class. In order to provide an independent confirmation of the scaling results, we turn to a direct thermodynamic calculation of the specific-heat exponent. The thermodynamic free energy is obtained from a transfer matrix formalism, which had been previously introduced for spin systems, and is now extended to the two-polymer model with aperiodic interactions.