Overlap equivalence in the Edwards-Anderson model.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Disordered Systems

Background:

• The Edwards-Anderson model is a fundamental model for spin glasses.
• Understanding the low-temperature phase of spin glasses is a key challenge in condensed matter physics.
• Relative fluctuations of overlap measures are crucial for characterizing spin glass phases.

Purpose of the Study:

• To investigate the relationship between link overlap and square standard overlap in the 3D Gaussian Edwards-Anderson model.
• To determine the equivalence of these two overlap measures in describing the low-temperature phase.
• To challenge the conventional 'trivial-nontrivial' picture of spin glass phases.

Main Methods:

• Analysis of the correlation coefficient between link overlap and square standard overlap.
• Examination of fluctuations in link overlap for fixed square standard overlap at large volumes.
• Scaling analysis of conditional variance in the thermodynamic limit.

Main Results:

• The link overlap and square standard overlap are uncorrelated above the critical temperature.
• Below the critical temperature, link overlap fluctuations vanish for fixed square standard overlap and large volumes.
• Conditional variance scales to zero in the thermodynamic limit, indicating a strong correlation between the two overlap measures.

Conclusions:

• The 'trivial-nontrivial' picture of spin glass phases is inconsistent with the observed behavior.
• The link overlap and square standard overlap are completely equivalent in describing the low-temperature phase of the Edwards-Anderson model.
• These findings necessitate a re-evaluation of the fundamental properties of spin glass phases.