Computing Boolean Statistical Models

141 Pages·1991·4.817 MB·English

by  Paulo Murilo Castro De Oliveira

Computing Boolean Statistical Models
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Computing
Boolean
Statistical
Models
Paulo Murilo Castro de Oltvelra
Institute de Fisica
Universidade Federal Fluminense
Brazil
World Scientific
Singapore • New Jersey • London • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128, Fairer Road, Singapore 9128
USA office: 687 Hartwell Street, Teaneck, NJ 07666
UK office: 73 Lynton Mead, Totteridge, London N20 8DH
COMPUTING BOOLEAN STATISTICAL MODELS
Copyright © 1991 by Worid Scientific Publishing Co. Ptc. Ltd,
AJl rights reserved. This book, or parts thereof, may not be reproduced in any form
orbyanymeans,eUctronicormechaniail,includingphotocopyingreconUngorany
t
information storage and retrieval system now known or to be invented, without
written permission from the Publisher.
ISBN 981-02-0238-5
Printed in Singapore by JBW Printers & Binders Pte. Ltd.
To Luts Indcio Lula da Silva
In memoriam of Francisco Mendes Filho
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Preface
In the last decade, we have seen great development in statistical physics
in terms of the linking with other fields of human knowledge and the
introduction of new investigation techniques. In particular, the use of com­
putational tools is now of fundamental importance in the study of the new
subjects recently introduced under the denomination of complex systems.
Both completely new concepts as the fractal behavior of nature as well as
old problems like magnetic odd properties observed in disordered materials
are now studied worldwide through computer work. Following the cur­
rent trend, this development will even accelerate in the near future. New
efficient techniques to deal with those systems using conventional comput­
ers are more and more important today. The purpose of this text is to
introduce some strategies in order to efficiently perform this kind of work.
These techniques are applied to some problems of statistical physics having
in common the Boolean (only two states) character of the individual units
that must be assembled together in forming complex macroscopic systems.
Besides this common feature, these problems are very distinct in what con­
cerns their applications and the kind of people that may be interested in
them.
This text is intended mainly for physicists, but also to other people
interested in these subjects, as biologists, computer scientists, mathemati­
cians, and others. The author has been involved in researches in these
subjects, and the text is a review of this work. It is written
using no technical details, and no specific knowledge is needed to under­
stand it. There are a lot of exercises whose solutions are presented in the
appendix. In my opinion, more and more people from different areas will be
involved in the studies of such complex systems in the near future. For this
reason, I think this text may be useful, mainly because the numerical work
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viii Computing Boolean Statistical Models
is performed on personal computers (I have an old 16-bit IBM PC running
at a frequency of 4.77 MHz with a memory of only 640 Kilobytes), using
standard languages as FORTRAN, PASCAL and C.
The reader will find terms like "we obtained" and "our results" along
the text. This is because the original works in which the present text is
based are not individual. I would like to acknowledge my various collabo­
rators from whom I learned most of the material revised in this text. They
are C. Tsallis, A. A. Gomes, G. Schwachheim, A. N. Chame, S. L. A.
de Queiroz, R. R. dos Santos, M. A. Continentino, R. M. Zorzenon and
F. C. Sa Barreto. Special thanks must be addressed to T. J. P. Penna
and S. M. Moss de Oliveira who performed the main work leading to the
results appearing in the last two chapters, respectively. Besides these col­
leagues, I also profited from discussions with many non-formally collabora­
tors. I wish to thank explicitly H. J. Herrmann, E. M. F. Curado, A. C. N.
de Magalhaes, A. M. Mariz, J. R. Drugowich de Felicio, N. Caticha, S.
Goulart Rosa, Jr., B. Boechat, E. V. L. de Mello, S. G. Coutinho, J. K.
Leal da Silva, R. M. C. de Almeida, S. R. A. Salinas, F. C. Alcaraz and D.
Stauffer. My various mistakes in both the concepts and the English usage
were eliminated from the original text by S. L. A. de Queiroz, S. M. Moss
de Oliveira and L. E. M. C. de Oliveira. Because of the great extent of these
mistakes, these colleagues are not responsible for the errors that remain in
this final version.
Rio de Janeiro
July, 1990
Contents
Preface vii
Chapter I Introduction .. 1
Chapter II Small Lattices 11
Chapter III Monte-Carlo Simulations ..,,. 21
Chapter IV Disorder and Frustration 33
Chapter V Cellular Automata 45
Chapter VI Neural Networks 61
Chapter VII Diluted Antiferromagnets 77
Appendix: Answers to All the Exercises 103
References 127
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