Computer Studies of Phase Transitions and Critical Phenomena: (Scientific Computation)

This book is based on research carried out by the author in close collabora- tion with a number of colleagues. In particular, I wish to thank Per Bak, A. John Berlinsky, Hans C. Fogedby, Barry Frank, S. 1. Knak Jensen, David Mukamel, David Pink, and Martin Zuckermann for fruitful and extremely stimulating cooperation. It is a pleasure for me to note that active interaction with most of these colleagues is still continuing. The work has been performed at several different institutions, notably the Department of Chemistry, Aarhus University, Denmark, and the Depart- ment of Physics, University of British Columb~a, Canada. I wish to thank the Department of Chemistry at Aarhus University for providing me with splen- did research facilities over the years. From May 1980 to August 1981, I visited the Department of Physics at the University of British Columbia and I would like to express my sincere gratitude to members ofthe department for provi- ding me with excellent working conditions. My special thanks are due to Professor Myer Bloom who introduced me to the field of phase transitions in biological membranes and in whose biomembrane group I found an extre- mely stimulating scientific atmosphere happily married with a most agreeable social climate. During the last two years when a major part ofthis work was carried out, I was supported by AlS De Danske Spritfabrikker through their Jubilreumsle- gat of 1981. Their support is gratefully acknowledged.

Table of Contents:
1. Introduction.- 2. Computer Methods in the Study of Phase Transitions and Critical Phenomena.- 2.1 Statistical Mechanics and Phase Transitions.- 2.2 Numerical Simulation Techniques.- 2.3 Exact Configurational Counting and Series Expansions.- 3. Monte Carlo Pure-model Calculations.- 3.1 Critical Behavior of the Three-dimensional Ising Model.- 3.2 Phase Behavior of Ising Models with Multi-spin Interactions.- 3.3 Thermodynamics of One-dimensional Heisenberg Models.- 4. Testing Modern Theories of Critical Phenomena.- 4.1 Fluctuation-induced First-order Phase Transitions.- 4.2 Critical Phenomena at Marginal Dimensionality.- 4.3 Basic Assumptions of Critical Correlation Theories.- 5. Numerical Experiments.- 5.1 Phase Transitions in Lipid Bilayers and Biological Membranes.- 5.2 Nuclear Dipolar Magnetic Ordering and Phase Transitions.- 5.3 Phase Transitions of Adsorbed Monolayers.- 5.4 Kinetics of Growth.