Statistical Mechanics

Fundamentals and Model Solutions

Teunis C Dorlas

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367478810
• eBook ISBN: 9781000375848
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Computer Science General

Statistical Mechanics: Fundamentals and Model Solutions, Second Edition

Fully updated throughout and with new chapters on the Mayer expansion for classical gases and on cluster expansion for lattice models, this new edition of Statistical Mechanics: Fundamentals and Model Solutions provides a comprehensive introduction to equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. The author presents a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. With problems and solutions, the book clearly explains the role of models for physical systems, and discusses and solves various models. An understanding of these models is of increasing importance as they have proved to have applications in many areas of mathematics and physics.

Features

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• Updated throughout with new content from the field

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• An established and well-loved textbook

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• Contains new problems and solutions for further learning opportunity

Author

Professor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.

III

Models in Statistical Mechanics

As mentioned in the introduction to this course, models are caricatures of physical systems designed to isolate and understand the principal reasons for physical phenomena. In statistical mechanics, phase transitions in particular are phenomena that are still poorly understood from the microscopic point of view. In this final part of the course we consider some simple models and determine their thermodynamic behaviour from the rules of statistical mechanics developed in Part II. These will also illustrate how phase transitions can come about.

In chapter 27 we consider a very simple model for rubber elasticity. Rubber consists of long chain molecules which are linked together at a few points by cross links. We model each section of a chain by a random walk. In chapter 28 we consider the Ising model for a ferromagnet. We show that it can be solved exactly in one dimension by means of a trick: the so-called transfer matrix. In two dimensions it can still be solved by essentially the same trick but the transfer matrix is then infinite-dimensional and one has to determine its maximum eigenvalue. This is possible but very difficult. We there...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Introduction
• Acknowledgments
• Section I Thermodynamics
• Section II Fundamentals of Statistical Mechanics
• Section III Models in Statistical Mechanics
• Appendix A Probability Theory
• Appendix B Quantum Mechanics
• Appendix C Convexity
• Index