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Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics

  • Errico Presutti

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Statistical Mechanics of Ising systems

  3. Mesoscopic Theory, non-local functionals

  4. Phase transitions in systems with Kac potentials

  5. Back Matter
    Pages 434-469

About this book

Introduction

Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

Keywords

Gamma convergence Ising models Kac potentials LMP model Potential Statistical mechanics generalized Pirogov-Sinai theory non local free energy functionals partial differential equation phase transitions in the continuum probabilistic methods

Authors and affiliations

  • Errico Presutti
    • 1
  1. 1.Dipartimento di MatematicaUniversitàdi Roma Tor VergataRomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-73305-8
  • Copyright Information Springer Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-73304-1
  • Online ISBN 978-3-540-73305-8
  • Series Print ISSN 1864-5879
  • Buy this book on publisher's site
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