Malte Henkel Libros

Critical phenomena occur in diverse physical systems, including liquid-vapor critical points, paramagnetic-ferromagnetic transitions, multicomponent fluids, alloys, superfluids, superconductors, polymers, and fully developed turbulence, extending even to the quark-gluon plasma and the early universe. Early theoretical approaches sought to simplify these complexities using a limited number of degrees of freedom, exemplified by the van der Waals equation and mean field approximations, culminating in Landau's general theory. Today, it is recognized that these phenomena share a common foundation in the strong fluctuations of infinitely many coupled variables. This understanding was first articulated through Onsager's exact solution of the two-dimensional Ising model. Subsequent advancements have led to scaling theories and the renormalization group, which provide precise descriptions near critical points, often aligning well with experimental results. Unlike the general perspective from a century ago, current insights emphasize that fluctuations occur across all length scales at critical points, highlighting the scale invariance of systems in such states. Additionally, conformal invariance allows for non-uniform, local rescaling as long as angles remain unchanged.

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.

KlappentextUnderstanding cooperative phenomena far from equilibrium is one of fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference for postgraduate students and nonspecialist researchers from related fields, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems. Lecture 1 gives an introduction and overview of the time-dependent behaviour of magnetic spin glasses. Lecture 2 is devoted to an in-depth discussion on the nature of the thermal glass-transition in structural glasses. Lecture 3 examines the glassy behaviour of granular systems. Lecture 4 gives a thorough introduction to the techniques and applications of Monte-Carlo simulations and the analysis of the resulting data through scaling methods. Lecture 5 introduces the zero-range-process concept as simple but subtle model to describe a range of static and dynamic properties of glassy systems. Lecture 6 shows how familiar RG methods for equilibrium systems can be extended to systems far from equilibrium.

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