Multifractal phase transitions in the non-debye relaxation processes

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Materials science

Background:

• Dielectric relaxation processes often deviate from simple Debye models.
• Understanding the complex dynamics of relaxation times is crucial.
• Fractal concepts offer new perspectives on disordered systems.

Purpose of the Study:

• To analytically derive multifractal measures for non-Debye dielectric relaxation.
• To investigate the multifractal thermodynamics and fractal scaling properties.
• To establish connections between fractal models and empirical dielectric relaxation formulas.

Main Methods:

• Analytical derivation of multifractal measures for relaxation-time distributions.
• Analysis of multifractal thermodynamics and scaling behavior.
• Investigation of Lipschitz-Hold singular exponents and shape parameters.

Main Results:

• Multifractal measures of relaxation-time distributions were obtained for non-Debye processes.
• Fractal scaling was demonstrated for relaxation times near distribution poles.
• A direct link was established between fractal exponents and empirical shape parameters.
• Generalized multifractal phase transitions with novel features were identified.

Conclusions:

• The study provides a theoretical framework for understanding complex dielectric relaxation using multifractal analysis.
• Fractal models offer analytical support for empirical dielectric relaxation formulas.
• The findings suggest potential applications in analyzing phase transitions in materials like organic glasses.