Strange Attractor in the Potts Spin Glass on Hierarchical Lattices

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.

6 pages, 4 figures, to appear in Physics Letters A 2013

References in corpus (8)

• Monte Carlo Study of Phase Transitions in the Bond-Diluted 3D 4-State Potts Model
• Dynamical critical exponents for the mean-field Potts glass
• The Spin Glass Phase in the Four-State, Three-Dimensional Potts Model
• Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study
• Critical Behavior of Three-Dimensional Disordered Potts Models with Many States
• Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit
• Potts spin glasses with 3, 4 and 5 states near $T=T_c$: expanding around the replica symmetric solution
• Continuous RSB mean-field solution of the Potts glass

Cited by in corpus (4)

• Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• Phase Transitions between Different Spin-Glass Phases and between Different Chaoses in Quenched Random Chiral Systems
• Devil's Staircase Continuum in the Chiral Clock Spin Glass with Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions