A Quantitative Clustering Approach to Ultrametricity in Spin Glasses

Abstract

We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the elimination of the (in this context accidental) spin flip symmetry plays a crucial role in the analysis, since the symmetry hides the real nature of the data. We are able to use in the analysis disorder averaged quantities. We are able to exhibit a number of features of the low $T$ phase of the mean field theory, and to claim that the full hierarchical structure can be observed without ambiguities only on very large lattice volumes, not currently accessible by numerical simulations.

arXiv comment15 pages with color figures

References in corpus (7)

• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• Data clustering and noise undressing for correlation matrices
• Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin Glasses
• Overlap Among States at Different Temperatures in the SK Model
• Ultrametricity in 3D Edwards-Anderson spin glasses
• A Numerical Study of Ultrametricity in Finite Dimensional Spin Glasses
• Equilibrium valleys in spin glasses at low temperature

Cited by in corpus (3)

• Spatial correlation functions in 3-d Ising spin glasses
• Solution-space structure of (some) optimization problems
• Ultrametricity of optimal transport substates for multiple interacting paths over a square lattice network