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Updated: Oct 16, 2025

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

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Sherrington-Kirkpatrick model for spin glasses: Solution via the distributional zeta function method.

C D Rodríguez-Camargo^1,2, E A Mojica-Nava^2,3, N F Svaiter⁴

¹Centro de Estudios Industriales y Logísticos para la productividad (CEIL, MD), Programa de Ingeniería Industrial, Corporación Universitaria Minuto de Dios, Bogotá AA 111021, Colombia.

Physical Review. E

|October 16, 2021

Summary

The distributional zeta function method reveals the complex multivalley structure of spin glasses. This approach provides exact expressions for equilibrium states and critical temperatures, enhancing our understanding of spin glass behavior.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics

Background:

Spin glasses present complex energy landscapes with multiple metastable states.
Understanding the thermodynamics and equilibrium properties of spin glasses is a significant challenge.

Purpose of the Study:

To apply the distributional zeta function method (DZFM) to the Sherrington-Kirkpatrick model of spin glasses.
To analyze the multivalley structure, equilibrium states, and critical properties of spin glasses.

Main Methods:

Utilizing the distributional zeta function method (DZFM) to analyze the spin glass model.
Calculating moments of the partition function to derive free energy contributions.
Determining saddle points and critical temperatures.

Main Results:

The DZFM reveals the spin-glass multivalley structure and provides exact expressions for saddle points.
A global critical temperature is identified, indicating numerous stable or metastable equilibrium states.
Analytical expressions for order parameters near the critical point match phenomenological results.
Singular behavior in linear and nonlinear susceptibility at the critical temperature is observed.
A positive definite expression for entropy is derived, with ground-state entropy tending to zero as temperature approaches zero.

Conclusions:

The DZFM offers a robust framework for studying spin glasses, accurately describing their complex equilibrium properties.
The method provides insights into the stability of solutions and the behavior of order parameters and entropy.
The findings contribute to a deeper theoretical understanding of disordered magnetic systems.