Numerical Methods in the Study of Critical Phenomena

1. Front Matter

   Pages I-IX

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2. Mathematical Methods

   1. Front Matter

      Pages 1-1

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   2. Study of Singularities

      1. Padé-Hermite Approximants

         • J. Della Dora

         Pages 3-11

      2. Some Comments About the Numerical Utilization of Factorial Series

         • J. P. Ramis, J. Thomann

         Pages 12-25

      3. Introduction to Real Quasianalytic Classes and Continuation Problems

         • T. Reboul

         Pages 26-36

   3. Critical Phenomena in Dynamical Systems

      1. Groups Transformations and Critical Asymptotics Applications to Non-Linear Differential and Partial Derivative Equations

         • J. R. Burgan, M. R. Feix, E. Fijalkow, M. P. Moraux, A. Munier

         Pages 37-46

      2. Antecedent Invariant Curves of an Endomorphism. Influence Domain of a Stable Cycle Coexisting with an Isolated Stable Invariant Curve

         • R. L. Clerc, Ch. Hartmann

         Pages 47-53

      3. Topological Entropy As a Measure of Dynamic Chaos in Endomorphisms

         • J. Couot, I. Gumowski, C. Gillot, C. Mira

         Pages 54-56

      4. Topological Entropy of Markov Processes for a C0- Endomorphism of the Interval

         • C. Gillot, G. Gillot

         Pages 57-63

      5. Sequential Iteration of Threshold Functions

         • E. Golès Chacc

         Pages 64-70

      6. Some Properties of Second Order Dynamic Systems with Parametric Resonances

         • I. Gumowski

         Pages 71-75

3. Applications in Physics

   1. Front Matter

      Pages 77-77

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   2. Critical Phenomena in Solid-State Physics

      1. On the Bifurcation of Certain Kam Tori in the Standard Mapping

         • S. Aubry

         Pages 79-80

      2. MO Stochasticity Criterion

         • R. Caboz, A. Lonke

         Pages 81-85

      3. Singularities in Saw Numerical Simulations

         • F. C. Cuozzo, E. E. Cambiaggio

         Pages 86-96

      4. Monte Carlo Measurement of the Single Vortex Free Energy in the Kosterlitz-Thouless Theory

         • H. J. Hilhorst, H. N. J. Vogelij, C. van Leeuwen, B. P. Th. Veltman

         Pages 97-103

      5. Algebraic Method for the Computation of the Partition Functions of Spin Glasses and Numerical Study of the Distributions of Zeros

         • B. Lacolle

         Pages 104-115

      6. Percolation and Gelation by Additive Polymerization

         • P. Manneville, L. de Sèze

         Pages 116-124

      7. Ground State Structure of the Random Frustration Model in Two Dimensions

         • R. Maynard, R. Rammal

         Pages 125-131

      8. Line Defects and the Glass Transition

         • N. Rivier, D. M. Duffy

         Pages 132-142

This volume contains most of the lectures presented at the meeting held in Carry-le­ nd Rouet from the 2 to the 4th June 1980 and entitled "Numerical Methods in the Study of Critical Phenomena". Scientific subjects are becoming increasingly differentiated, and the number of journals and meetings devoted to them is continually increasing. Thus it has become very difficult for the non-specialist to approach subjects with which he is not familiar. Hence the purpose of our meeting was to bring together scientists from different disciplines to study a common subject and to stimulate discussion' between participants. We hope this goal was reached. The lectures are grouped in five chapters and, inside the first and the second chapter, under two headings. In each group they are classified in alphabetical order by author. We are pleased to publish these Proceedings in a series whose multidisciplinary character has been emphasized from the beginning. We are indebted to all who provided us with their help, particularly to Mrs. A. Litman of the Centre International de Rencontres Mathematiques at Luminy (C.I.R.M.) whose kindness and efficiency are well known; from the practical point of view, the meetings were organized within the scientific framework of the G.I.S. No.19 (C.N.R.S.), with the participation of the University of Grenoble.

• Numerische Mathematik
• Phenomena
• Renormalization group
• bifurcation
• chaos
• dynamical system
• dynamical systems
• entropy
• invariant
• mechanics
• numerical analysis
• numerical method
• quantum chemistry
• solution
• statistical mechanics

• Laboratoire d’Informatique et de Mathématiques Appliquées de Grenoble, Université Scientifique et Médicale de Grenoble, Grenoble Cédex, France

  Jean Dora, Jacques Demongeot, Bernard Lacolle

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