Strange Attractor in the Potts Spin Glass on Hierarchical Lattices

TL;DR

This paper studies the behavior of the Potts spin glass model on hierarchical lattices, revealing a strange attractor at low temperatures indicating a condensed phase with algebraic decay.

Contribution

It provides an exact renormalization group analysis showing the existence of a strange attractor in the coupling distribution for the Potts spin glass on hierarchical lattices.

Findings

Strange attractor appears above a critical dimension for q>2.

The attractor is robust across different initial distributions.

Indicates a condensed phase with algebraic decay.

Abstract

The spin-glass $q$-state Potts model on $d$-dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension $d_l(q)$ for $q > 2$, the coupling constants probability distribution flows to a low-temperature \emph{strange attractor} or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature $T_c(q,d)$. The strange attractor was investigated considering four initial different distributions for $q = 3$ and $d = 5$ presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.