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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.
List of contents
Introduction.- Functional Renormalization Group of Disordered Systems.- Non-perturbative Renormalization Group.- Dimensional Reduction and Its Breakdown in the Driven Random Field O(N) Model.- Nonequilibrium Kosterlitz-Thouless Transition in the Three-dimensional Driven Random Field XY Model.- Summary and Future Perspectives.
About the author
Taiki Haga is a researcher at the Department of Physics, Kyoto University with a primary focus on non-equilibrium statistical mechanics. He received his Bachelor of Science from Tohoku University in 2013, and his Master and Doctor of Science from Kyoto University in 2015 and 2018, respectively. He was awarded a Research Fellowship for Young Scientists (DC1) by the Japan Society for the Promotion of Science (JSPS) and his research was supported by the JSPS from 2015 to 2018.
Summary
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.
