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Conformal invariants --- Critical phenomena (Physics)

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Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties.   Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.

Conformal invariants --- Stochastic processes --- Phase transformations (Statistical physics) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Physics - General --- Mathematical models --- Conformal invariants. --- Stochastic processes. --- Mathematical models. --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Random processes --- Conformal invariance --- Invariants, Conformal --- Physics. --- Mathematical physics. --- Statistical physics. --- Dynamical systems. --- Mathematical Methods in Physics. --- Statistical Physics, Dynamical Systems and Complexity. --- Mathematical Physics. --- Probabilities --- Conformal mapping --- Functions of complex variables --- Phase rule and equilibrium --- Statistical physics --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Physical mathematics --- Statistical methods --- Mathematics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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Mathematical physics --- Statistical physics --- theoretische fysica --- wiskunde

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This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed. The techniques used for directed percolation are then extended to other universality classes and many important results on model parameters are provided for easy reference.

Nonequilibrium statistical mechanics. --- Phase transformations (Statistical physics) --- Mathematical physics. --- Physical mathematics --- Physics --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Non-equilibrium statistical mechanics --- Statistical mechanics --- Mathematics --- Distribution (Probability theory. --- Statistical physics. --- Theoretical, Mathematical and Computational Physics. --- Probability Theory and Stochastic Processes. --- Condensed Matter Physics. --- Complex Systems. --- Numerical and Computational Physics, Simulation. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistical methods --- Probabilities. --- Condensed matter. --- Dynamical systems. --- Physics. --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Nonequilibrium statistical mechanics

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This book is Volume 2 of a two-volume set describing two main classes of non-equilibrium phase-transitions. This volume covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.

Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Probability theory --- Mathematics --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- Classical mechanics. Field theory --- Statistical physics --- Solid state physics --- Matter physics --- Physics --- Artificial intelligence. Robotics. Simulation. Graphics --- EMI (electromagnetic interference) --- materie (fysica) --- quantummechanica --- waarschijnlijkheidstheorie --- grafentheorie --- theoretische fysica --- stochastische analyse --- statistiek --- simulaties --- wiskunde --- fysica --- kansrekening --- dynamica --- Phase transformations (Statistical physics) --- Nonequilibrium statistical mechanics