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Discrete Mathematics in Statistical Physics

Introductory Lectures

  • Textbook
  • © 2010

Overview

Authors:
  1. Martin Loebl

    1. Department of Applied Mathematics, Institut of Theoretical Computer Science, Charles University, Praha, Tschechische Republik

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  • Die Brücke zwischen Diskreter Mathematik und Statistischer Physik

Part of the book series: Advanced Lectures in Mathematics (ALM)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Basic concepts

    • Martin Loebl
    Pages 1-11

  3. Introduction to Graph Theory

    • Martin Loebl
    Pages 13-49

  4. Trees and electrical networks

    • Martin Loebl
    Pages 51-64

  5. Matroids

    • Martin Loebl
    Pages 65-75

  6. Geometric representations of graphs

    • Martin Loebl
    Pages 77-100

  7. Game of dualities

    • Martin Loebl
    Pages 101-117

  8. The zeta function and graph polynomials

    • Martin Loebl
    Pages 119-139

  9. Knots

    • Martin Loebl
    Pages 141-155

  10. 2D Ising and dimer models

    • Martin Loebl
    Pages 157-171

  11. Back Matter

    Pages 173-187
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Keywords

About this book

The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently.
It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.

Basic concepts - Introduction to Graph Theory - Trees and electrical networks – Matroids - Geometric representations of graphs - Game of dualities - The zeta function and graph polynomials – Knots - 2D Ising and dimer models

- Advanced Graduate Students in Mathematics, Physics and Computer Sciences
- Researchers

Prof. Dr. Martin Loebl, Dept. of Mathematics, Charles University, Prague

Authors and Affiliations

  • Department of Applied Mathematics, Institut of Theoretical Computer Science, Charles University, Praha, Tschechische Republik

    Martin Loebl

About the author

Prof. Dr. Martin Loebl, Dept. of Mathematics, Charles University, Prague

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