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Recently, interacting particle systems have been studied widely from the standpoints of mathematics, physics, chemistry and biology. This book examines the phase transitions of interacting particle systems, especially their critical values and order parameters, and poses the following question: how can researchers obtain good bounds on the critical values and the order parameters?

This volume contains the notes of lectures given at the School Quantum Potential Theory: Structure and Applications to Physics . This school was held at the Alfried Krupp Wissenschaftskolleg in Greifswald from February 26 to March 9, 2007. We thank the lecturers for the hard work they - complished in preparing and giving these lectures and in writing these notes. Theirlecturesgiveanintroductiontocurrentresearchintheirdomains, which is essentially self-contained and should be accessible to Ph.D. students. We hope that this volume will help to bring together researchers from the areas of...