Numerical Methods in the Study of Critical Phenomena

1. Mathematical Methods.- 1.1 Study of Singularities.- Padé-Hermite Approximants.- Somme Comments About the Numerical Utilization of Factorial Series.- to Real Quasianalytic Classes and Continuation Problems.- 1.2 Critical Phenomena in Dynamical Systems.- Groups Transformations and Critical Asymptotics Applications to Non-Linear Differential and Partial Derivative Equations.- Antecedent Invariant Curves of an Endomorphism. Influence Domain of a Stable Cycle Coexisting with an Isolated Stable Invariant Curve.- Topological Entropy As a Measure of Dynamic Chaos in Endomorphisms.- Topological Entropy of Markov Processes for a C0-Endomorphism of the Interval.- Sequential Iteration of Threshold Functions.- Some Properties of Second Order Dynamic Systems with Parametric Resonances.- 2. Applications in Physics.- 2.1 Critical Phenomena in Solid-State Physics.- On the Bifurcation of Certain Kam Tori in the Standard Mapping.- MO Stochasticity Criterion.- Singularities in Saw Numerical Simulations.- Monte Carlo Measurement of the Single Vortex Free Energy in the Kosterlitz-Thouless Theory.- Algebraic Method for the Computation of the Partition Functions of Spin Glasses and Numerical Study of the Distributions of Zeros.- Percolation and Gelation by Additive Polymerization.- Ground State Structure of the Random Frustration Model in Two Dimensions.- Line Defects and the Glass Transition.- Universality in Size-Effects in 2D Percolation.- 2.2 Use of Renormalisation Techniques.- The Phenomenological Renormalization Method.- Computation of the Yang-Lee Edge Singularity in Ising Models.- Real-Space Renormalization-Group Method for Quantum Systems: Application to Quantum Frustration in Two Dimensions.- Yang-Lee Edge Singularity by Real Space Renormalization Group.- 3. Applications inBiology.- Numerical Determination of a Periodical Solution of Discontinuous Type, near a Singular Point, for a Neurophysiological Model.- On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations.- Critical Delays in Logical Asynchronous Models.- 4. Applications in Chemistry.- A Simulation Technique for Studying Critical Properties of Chemical Dissipative Systems.- Critical Paths and Passes: Application to Quantum Chemistry.- 5. Non-Physical Applications of Statistical Mechanics.- Telephone Network: Statistical Mechanics and Non-Random Connecting Procedures.- The Thermodynamic Formalism in Population Biology.- Asymptotic Inference for Markov Random Fields on Zd.- List of Contributors.