This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-Tc superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.

Patterns are becoming the focal point of many areas of scientific endeavour in recent years owing to the progress of computer science, laboratory experiments and observations, and analytical tools. This book brings together articles by the leading experts in this field. The following topics are discussed in this volume: current status of pattern research with emphasis on real phenomena and new theoretical concepts; interdisciplinary subjects involving Statistical Physics, Condensed Matter Physics, Fluid Mechanics, Nonequilibrium and Nonlinear Phenomena.

Speech by Toyosaburo Taniguchi Dr. Kubo, Chairman, Distinguished Guests, and Friends, I am very happy, pleased and honored to be here this evening with so many distinguished guests, friends, and scholars from within this country and from different parts of the world. The Taniguchi Foundation wishes to extend a warm and sincere welcome to the many participants of the Ninth International Symposium on the Theory of Condensed Matter, which se ries was inaugurated eight years ago through the strenuous efforts of Dr. Ryogo Kubo, who is gracing us today with his presence. We are deeply indebted to Dr. Kubo, Dr. Suzuki, and their associates, who havE' spent an enormous amount of time and effort to make this particular symposium possible. We are convinced that the foundation should not be considered as what makes our symposium a success. The success is entirely due, I feel, to the continuous efforts of the Organizing Committee and of all those who have lent their support to this program. In this sense, your words of praise about the symposium, if any, should be directed to all of them. So far, I have met in person a total of 62 participants in this Division from 12 countries: Argentina, Belgium, Canada, Denmark, the Federal Republic of Germany, France, Ireland, Israel, Rumania, Switzerland, the United Kingdom, and the United States of America, with 133 participants from Japan. Those friends I have been privileged to make, I shall always treasure."

Dr. Yoshio Nishina was a key figure in modem physics in Japan and a world pioneer in many fields of modem science such as nuclear physics, cosmic-ray physics, and radiobiology. He devoted his life to the development of science, so that his beloved country could compete with any other country in science and technology. Unfortunately, he died soon after the Second World War and did not witness the results of his great efforts. To commemorate the centennial of Dr. Nishina' s birth, a Nishina Centennial Symposium was held in Tokyo from December 5 to 7, 1990, under the co-sponsorship of the Nishina Memorial Foundation and RIKEN (the Institute of Physical and Chemical Research). The symposium was entitled Evolutionary Trends in the Physical Sciences. The title of the symposium was very broad and ambitious. Indeed, progress in physics over recent decades has been truly amazing, so much so that the present frontiers of physics extend far beyond the horizons we saw when we were young. Experiments in particle physics have revealed many new particles, and may eventually lead to the clarification of the ultimate structure of matter, though it is not known whether man will ever fully understand how natural forces are unified. At the same time, it is becoming more and more likely that the creation of the universe will finally be discovered by continuing the lines of research into physics that have been pursued over the past decades.