Leuzzi / Nieuwenhuizen Thermodynamics of the Glassy State

Erscheinungsjahr 2007
ISBN: 978-1-4200-1243-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 368 Seiten

Reihe: Condensed Matter Physics

In the past thirty years, the area of spin glasses has experienced rapid growth, including the development of solvable models for glassy systems. Yet these developments have only been recorded in the original research papers, rather than in a single source. Thermodynamics of the Glassy State presents a comprehensive account of the modern theory of glasses, starting from basic principles (thermodynamics) to the experimental analysis of one of the most important consequences of thermodynamics-Maxwell relations.

After a brief introduction to general theoretical concepts and historical developments, the book thoroughly describes glassy phenomenology and the established theory. The core of the book surveys the crucial technique of two-temperature thermodynamics, explains the success of this method in resolving previously paradoxical problems in glasses, and presents exactly solvable models, a physically realistic approach to dynamics with advantages over more established mean field methods. The authors also tackle the potential energy landscape approach and discuss more detailed theories of glassy states, including mode coupling, avoided critical point, replica, and random first order transition theories.

This reference lucidly explores recent theoretical advances in the thermodynamics of slowing-aging (glassy) systems. It details the general properties of glassy states while also demonstrating how these properties are present in specific models, enabling readers to thoroughly understand this fundamental yet challenging area of study.

Zielgruppe

Researchers and graduate students in materials science and physics, in particular, those working on the theory of glassy systems and the related field of spin glasses.

Autoren/Hrsg.

Leuzzi, Luca

Nieuwenhuizen, Th. M

Fachgebiete

• Naturwissenschaften Physik Thermodynamik

Inhaltsverzeichnis

INTRODUCTION

THEORY AND PHENOMENOLOGY OF GLASSES
Processes, time-scales, and transitions
Strong and fragile glass formers
Aging
Configurational entropy
Adam-Gibbs entropic theory
Fragility index
Kovacs effect

TWO TEMPERATURE THERMODYNAMICS
Elements of thermodynamics
Fictive temperature
Two temperature thermodynamics
Laws of thermodynamics for off-equilibrium systems
Laws of thermodynamics for glassy magnets
Effective temperature in thermal cycles
Fluctuation formula and effective temperatures
Fluctuation and dissipation out of equilibrium
Direct measure of the effective temperature
Asymptotic solution in nonlinear cooling

EXACTLY SOLVABLE MODELS FOR THE GLASSY STATE
Harmonic oscillator model
Kinetic models with separation of timescales
Out-of-equilibrium thermodynamics
Below the Kauzmann transition
Kovacs effect: limits of two temperature thermodynamics
Measuring effective temperature in HO models
Mode-dependent effective temperature
HOSS equations of motion for one-time variables
Monte Carlo integrals in one- and two-time dynamics

AGING URN MODELS
The backgammon model
Two-time dynamics and FDR effective temperature
A model for collective modes
Occupation probability density equations
Ansatz for the adiabatic approximation
Approach to equilibrium of occupation densities
Probability distribution of proposed energy updates

GLASSINESS IN A DIRECTED POLYMER MODEL
The directed polymer model
Directed polymer dynamics
Cooling and heating setups

POTENTIAL ENERGY LANDSCAPE APPROACH
Potential energy landscape
Thermodynamics in supercooled liquids
The solid amorphous phase
Fragility in the PEL
PEL approach to the random orthogonal model
PEL approach to the harmonic oscillator models
Many-body glassy models

THEORIES OF THE GLASSY STATE
Mode coupling theory
Replica theory for glasses with quenched disorder
Glass models without quenched disorder: clone theory
Frustration limited domain theory
Random first order transition theory

BIBLIOGRAPHY

INDEX