Single replica spin-glass phase detection using field variation and machine learning

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Computational physics

Background:

• The Sherrington-Kirkpatrick (SK) model is a fundamental model in statistical mechanics for studying spin glasses.
• Traditional phase transition detection in the SK model relies heavily on computationally intensive replica-based methods.
• The intrinsic phase of a system exists independently of the replica method used for its detection.

Purpose of the Study:

• To propose a novel, computationally efficient method for detecting phase transitions in the SK spin-glass model.
• To demonstrate that local field variations within a single replica can effectively distinguish between different phases.
• To develop a machine learning algorithm for generating the SK model's phase diagram using this new method.

Main Methods:

• Analysis of the mean and variance of local fields experienced by individual spins in a single replica configuration.
• Development of a machine learning algorithm trained on local field statistics.
• Comparison of the algorithm-generated phase diagram with established theoretical solutions for the SK model.

Main Results:

• The mean and variance of local fields serve as robust indicators for distinguishing ferromagnetic, paramagnetic, and spin-glass phases.
• The developed machine learning algorithm accurately reproduces the theoretical phase diagram of the SK model.
• The proposed method demonstrates significant computational efficiency compared to replica-based techniques.

Conclusions:

• Local field analysis in a single replica provides an effective and efficient approach for phase detection in spin-glass systems.
• This novel method offers a viable alternative for mapping complex phase diagrams, particularly in computationally demanding scenarios.
• The findings pave the way for more accessible studies of phase transitions in disordered magnetic systems.