Ground-state phase-space structures of two-dimensional ±J spin glasses: A network approach

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Network Science

Background:

• Spin glasses are complex magnetic materials with disordered interactions.
• Understanding their ground-state phase space is crucial for characterizing their behavior.
• Previous studies often relied on simulations or limited analytical methods.

Purpose of the Study:

• To develop and apply a complex-network approach for analyzing spin glass phase spaces.
• To uncover fundamental properties of spin glass ground states and their dynamics.
• To investigate the topological characteristics of spin glass phase space networks.

Main Methods:

• Exact mapping of ground-state phase spaces of 2D Edwards-Anderson bimodal spin glasses to networks.
• Analysis of network properties including connectivity distribution, spectra, community structures, and fractal dimensions.
• Construction of a coarse-grained network representing the entropy landscape.

Main Results:

• Phase-space networks exhibit Gaussian connectivity distributions and spectra, indicative of specific microstate visiting frequencies.
• Discovery of community structures within phase-space networks, leading to a scale-free entropy landscape network.
• Phase-space networks demonstrate fractal structures, linked to the rugged entropy landscape.
• Significant changes in network properties (connectivity, community, fractal) observed at the ferromagnetic-to-glass phase transition.

Conclusions:

• The complex-network approach provides quantitative insights into spin glass ground states.
• Spin glass phase-space networks form a distinct class of complex networks with unique topology.
• These findings offer a novel perspective on the statistical mechanics of disordered systems.