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Counting multiple solutions in glassy random matrix models.

¹Poornaprajna Institute for Scientific Research, Bangalore 560080, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 4, 2003

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This study counts multiple solutions in glassy random matrix models by transforming the problem into a moment problem. The number of moments grows exponentially with matrix size, suggesting implications for supercooled liquids.

Area of Science:

Statistical Mechanics
Condensed Matter Physics
Random Matrix Theory

Background:

Glassy random matrix models are used to study structural glasses in the high-temperature phase.
Previous work by Brézin and Deo (1999) raised puzzles regarding these models.

Purpose of the Study:

To count the number of multiple solutions in specific glassy random matrix models.
To investigate the role of asymmetry (tapping) in generating these solutions.

Main Methods:

Reducing the problem of counting multiple solutions to a moment problem.
Analyzing the behavior of moments under the introduction and vanishing of asymmetry.

Main Results:

The number of moments grows exponentially with the matrix size (N).

Related Experiment Videos

The nature of the asymmetry is critical for identifying multiple solutions.

Conclusions:

The findings offer a method for counting solutions in random matrix models.
Results may have implications for understanding the supercooled liquid phase in spin glass models.