State Hierarchy Induced by Correlated Spin Domains in short range spin glasses

Abstract

We generate equilibrium configurations for the three and four dimensional Ising spin glass with Gaussian distributed couplings at temperatures well below the transition temperature T_c. These states are analyzed by a recently proposed method using clustering. The analysis reveals a hierarchical state space structure. At each level of the hierarchy states are labeled by the orientations of a set of correlated macroscopic spin domains. Our picture of the low temperature phase of short range spin glasses is that of a State Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low temperature phase is manifest in the fact that the composition of such a spin domain (i.e. its constituent spins), as well as its identifying label, are defined and determined by the ``location'' in the state hierarchy at which it appears. Mapping out the phase space structure by means of the orientations assumed by these domains enhances our ability to investigate the overlap distribution, which we find to be non-trivial. Evidence is also presented that these states may have a non-ultrametric structure.

30 pages, 17 figures

References in corpus (2)

• Interfaces (and Regional Congruence?) in Spin Glasses
• Correct extrapolation of overlap distribution in spin glasses

Cited by in corpus (9)

• Collective Decision Dynamics in the Presence of External Drivers
• Hierarchical landscape of hard disk glasses
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Non-trivial link overlap distribution in three-dimensional Ising spin glasses
• Spin-glass chain in a magnetic field : influence of the disorder distribution on ground state properties and low-energy excitations
• Dealing with correlated choices: How a spin-glass model can help political parties select their policies
• On the quantum behavior and clustering properties of correlated financial portfolios