Universalities in Condensed Matter

Universality is one of the fascinating features of condensed matter physies: it is the property whereby systems of radieally different composition and structure ex hibit similar behavior. In the mid-1960s the word entered usage to express the fact that the equations of state of several substances could be mapped onto one another near the critical point: critieal universality. Renormalization group theory in the early 1970s provided both an explanation and a sharper definition of universality. Systems with similar behavior - universality classes - correspond to the same fixed point of a renormalization group transformation. A number of brilliant con tributions showed how the same concepts could be applied to non-thermodynamie systems, such as the statisties of self-avoiding walks or of connected clusters on a lattice. A few years later it was realized that chaotie dynamieal systems mayaiso exhibit some degree of universality, the paradigmatic example being the period doubling cascade in the iterated maps of the unit interval into itself.

Autorentext
Dr. Nino Boccara is Professor Emeritus of Physics at the University of Illinois at Chicago, Professor Emeritus of Mathematics at the Ecole Supérieure de Physique et Chimie de la Ville de Paris, and Former Director of Research in Theoretical Physics at the CNRS.

Inhalt
I Geometrical Approaches.- Hierarchy of Line Defects in Structures.- Are There Universalities in Systems with Frustrated Local Order?.- Contribution to the Theory of Quasicrystal Approximants.- Beyond Quasiperiodicity: Scaling Properties of a Fourier Spectrum.- The Fibonacci Chain Quasicrystal: An Exact Decimation Approach.- II Critical Scaling.- Experimental Investigations of the Sol-Gel Transition.- Conformation, Connectivity and Mechanical Properties of Polycondensates Near the Gel Point.- Conformation and Dynamical Properties of Polymer Clusters in Concentrated Solution.- Percolation and Dispersive Conduction in Fluid-Saturated Porous Media.- Microscopic Observation of Critical Fluctuations: Fractal Aspects.- Some Static and Dynamic Results for Walks on the Lattice.- Problem of Universality in Phase Transitions in Low-Symmetry Systems.- Exact Critical Properties of Two-Dimensional Polymer Networks from Conformai Invariance.- A Hierarchical Schrödinger Operator.- Universality and Nonuniversality in Frustrated Smectics.- A Langevin Equation Approach to Sine-Gordon Soliton Diffusion with Application to Nucleation Rates.- Disorder, Frustration and Critical Exponents.- Universality Classes of Fluctuating Membranes.- Diffusion Fronts of Interacting Particles.- Static Scaling with Tc Positive, Null or Negative.- Magnetic Frustration and Pairing in Doped Lathanum Cuprate.- III Ramified Structures and Fractals.- On the Shape of Trees: Tools to Describe Ramified Patterns.- Scaling and Universality in Multifractal Growth Processes.- Theory of Fractal Growth.- The Hunt for Universality in Fracture.- Multifractal Viscous Fingering and Non-Newtonian Growth.- Scattering by Fractal Structures.- Capillary Aggregation at an Interface.- Kinetics of Aggregation in a Sheared Dispersionof Macroscopic Spheres.- Reaction-Limited Aggregation: Recent Simulation Results.- Cluster-Cluster Aggregation of Magnetic Particles.- Diffusion Limited Aggregation on the Torus.- Filtered Operators and Ultrametricity.- IV Anomalous Scaling Laws.- Random Multiplicative Processes and Multifractals.- Universal Properties of Multifractal Moments: Analogies with Critical Phenomena.- Multifractal Analysis in the Circle Map: Analogies with Critical Phenomena.- Correlations in Multifractals.- Bulk and Surface Exponents at the d=2 ?-Point.- Rough Surfaces: Scaling Theory and Universality.- Computer Simulation of Random Ballistic Deposition.- V Dynamical Systems and Turbulence.- Scaling Properties of Soft Thermal Turbulence in Rayleigh-Bénard Convection.- The Organization of Chaos by Periodic Orbits: Topological Universality of Complex Systems.- Some Results on Lyapunov Exponents for Products of Random Matrices.- Relevance of Classical Chaos in Quantum Mechanics.- Intermittency and Equilibrium Measures in Dynamical Systems.- Chaos in a Model of Random Neural Networks.- Phase Transitions on Strange Attractors and Fractal Aggregates.- Diffusion of Passive Scalars in Fluid Flows: Maps in Three Dimensions.- Gap Road: Main Properties.- Dynamics and Damage Spreading in Cooperative Systems: A Numerical Search for Universality.- Universality in Relaxation of Disordered Systems.- Index of Contributors.