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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

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Extreme value statistics distributions in spin glasses.

Michele Castellana¹, Aurélien Decelle, Elia Zarinelli

¹LPTMS, CNRS and Université Paris-Sud, UMR8626, Orsay, France. michele.castellana@lptms.u-psud.fr

Physical Review Letters

|January 17, 2012

Summary

This summary is machine-generated.

This study reveals the statistical distributions of the pseudocritical temperature in spin-glass models. The findings connect temperature fluctuations to extreme value statistics, offering insights into magnetic materials.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics

Background:

Spin-glass models like Sherrington-Kirkpatrick (SK) and Edwards-Anderson (EA) are crucial for understanding disordered magnetic systems.
Pseudocritical temperature fluctuations are key to characterizing phase transitions in these systems.

Purpose of the Study:

To investigate the probability distribution of the pseudocritical temperature in both mean-field (SK) and short-range (EA) spin-glass models.
To establish the connection between pseudocritical point fluctuations and extreme value statistics.

Main Methods:

Analysis of the Sherrington-Kirkpatrick model with Gaussian and binary couplings.
Statistical analysis of the Edwards-Anderson model.
Application of extreme value statistics to random variables.

Main Results:

The pseudocritical temperature distribution for the SK model follows the Tracy-Widom distribution.
The pseudocritical temperature distribution for the EA model is identified as the Gumbel distribution.
A direct link between pseudocritical temperature fluctuations and extreme value statistics was demonstrated.

Conclusions:

The study successfully characterized the probability distributions of the pseudocritical temperature in two fundamental spin-glass models.
The findings suggest that the pseudocritical point distribution in EA models, relevant to materials like iron manganese titanate and europium barium manganite, is experimentally measurable.