The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: entropy, universality, chaos and cascades in the renormalization group flow

2011/04/05 by Thomas Jorg, Thomas Jörg, Florent Krzakala · 18 citations
Materials Science · Physics and Astronomy · #Cascade #Critical phenomena #Entropy (arrow of time) #Fixed point #Limit (mathematics) #Material Dynamics and Properties #Quantum many-body systems #Renormalization #Renormalization group #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1088/1742-5468/2012/01/l01001

published in Journal of Statistical Mechanics Theory and Experiment 2012(01), L01001 (Institute of Physics) · 14 pages, 5 figures, 2 tables

arxiv created 2011/04/05 · openalex publication_date 2012/01/30 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

The properties of discrete two-dimensional spin glasses depend strongly on the way the zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal–Kadanoff renormalization group. We see, in particular, how these properties are connected with the presence of a cascade of fixed points in the renormalization group flow. Of particular interest are two unstable fixed points that correspond to two different spin-glass phases at zero temperature. We discuss how these phenomena are related with the presence of entropy fluctuations and temperature chaos, and universality in this model.

Citations

• Possible description of domain walls in two-dimensional spin glasses by stochastic Loewner evolutions
• Stiffness exponent of two-dimensional Ising spin glasses for nonperiodic boundary conditions using aspect-ratio scaling
• Ground-state clusters of two-, three-, and four-dimensional±JIsing spin glasses
• A cluster Monte Carlo algorithm for 2-dimensional spin glasses
• Entropic long range order in a 3D spin glass model
• Gibbs states and the set of solutions of random constraint satisfaction problems

Cited by

• An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study
• Bimodal and Gaussian Ising spin glasses in dimension two