Perturbation series expansion methods are sophisticated numerical tools used to provide quantitative calculations in many areas of theoretical physics. This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly correlated electron systems and elementary particles. Early chapters cover the classical treatment of critical phenomena through high-temperature expansions, and introduce graph theoretical and combinatorial algorithms. The book then discusses high-order linked-cluster perturbation expansions for quantum lattice models, finite temperature expansions, and lattice gauge models. Also included are numerous detailed examples and case studies, and an accompanying resources website, www.cambridge.org/9780521842426, contains programs for implementing these powerful numerical techniques. A valuable resource for graduate students and postdoctoral researchers working in condensed matter and particle physics, this book will also be useful as a reference for specialized graduate courses on series expansion methods.

• Hands-on approach, suitable for self-learning • A comprehensive guide to series expansion methods for lattice models in theoretical physics • Applications to models in condensed matter theory and particle physics • Computer programs for implementation of this powerful numerical technique are available at www.cambridge.org/9780521842426

### Contents

Preface; 1. Introduction; 2. High- and low-temperature expansions for the Ising Model; 3. Models with continuous symmetry and the free graph expansion; 4. Quantum spin models at T = 0; 5. Quantum antiferromagnets at T = 0; 6. Correlators, dynamical structure factors and multi-particle excitations; 7. Quantum spin models at finite temperature; 8. Electronic models; 9. Review of lattice gauge theory; 10. Series expansions for lattice gauge models; 11. Additional topics; Appendices; Bibliography; Index.