عنوان

Renormalization group analysis of nonequilibrium phase transitions in driven disordered systems /

9789811361715

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Renormalization group analysis of nonequilibrium phase transitions in driven disordered systems /

[Book]

Taiki Haga.

Singapore :

Springer,

2019.

1 online resource

Springer theses

"Doctoral thesis accepted by the Kyoto University, Kyoto, Japan."

Includes bibliographical references.

Intro; Supervisor's Foreword; Parts of this thesis have been published in the following journal articles:; Acknowledgements; Contents; 1 Introduction; 1.1 Physics of Phase Transitions; 1.2 Phase Transitions in Disordered Systems; 1.2.1 Models of Disordered Systems; 1.2.2 Imry and Ma's Argument; 1.2.3 Dimensional Reduction; 1.2.4 Other Models of Disordered Systems; 1.3 Disordered Systems Driven Out of Equilibrium; 1.3.1 Collective Transports in Random Media; 1.3.2 Phase Transitions in Driven Disordered Systems; 1.4 Purpose of This Study; 1.5 Outline of This Thesis; References

2 Functional Renormalization Group of Disordered Systems2.1 Why is the Functional Renormalization Group Treatment Necessary?; 2.2 FRG of the Random Manifold Model; 2.2.1 RG Equation of the Disorder Correlator; 2.2.2 Roughness Exponent Near Four Dimensions; 2.3 FRG of the Random Field and Random Anisotropy O(N) Models; 2.3.1 RG Equation of the Disorder Correlator; 2.3.2 Critical Exponents; 2.3.3 Fixed Point of the Random Field O(N) Model; 2.3.4 Fixed Point of the Random Anisotropy O(N) Model; References; 3 Nonperturbative Renormalization Group; 3.1 General Formalism; 3.1.1 Statics

5 Nonequilibrium Kosterlitz-Thouless Transition in the Three-Dimensional Driven Random Field XY Model5.1 Spin-Wave Calculation; 5.2 Numerical Simulation; 5.2.1 Correlation Function; 5.2.2 Phase Diagram; 5.3 RG Analysis of the Spin-Wave Model; 5.3.1 Exact Flow Equation for the Effective Action; 5.3.2 Flow Equations of the Disorder Cumulants; 5.3.3 RG Evolution of the Disorder Cumulants; 5.4 Effect of Vortices; References; 6 Summary and Future Perspectives; References

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This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz?Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.

Springer Nature

com.springer.onix.9789811361715

Renormalization group analysis of nonequilibrium phase transitions in driven disordered systems.

9789811361708

Broken symmetry (Physics)

Phase transformations (Statistical physics)

Mathematical Methods in Physics.

Phase Transitions and Multiphase Systems.

Statistical Physics and Dynamical Systems.

Broken symmetry (Physics)

Phase transformations (Statistical physics)

SCIENCE-- Energy.

SCIENCE-- Mechanics-- General.

SCIENCE-- Physics-- General.

PHS

PHS

SCI-- 024000

SCI-- 041000

SCI-- 055000

Haga, Taiki

20200823233532.0

pn

[Book]

Y