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9780199556632Mladinska knjiga ID
401257Leto izida
2010Velikost (šxdxv)
150 × 200 × 10Status dobavljivosti
Na zalogi pri dobaviteljuJezik
ANGTeža
300 gZaložnik
OXFORD UNIVERSITY PRESSAvtor
BARRY MCCOYOpis
This book presents the advances made in Statistical Mechanics of the last 50 years, including mathematical theorems on order and phase transitions; numerical and series computations of phase diagrams; and solutions for important solvable models including Ising and 8 vertex.Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last fifty years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum groups and affine Lie algebras. They have engendered remarkable discoveries concerning non-linear differential equations and algebraic geometry, and have produced profound insights in both condensed matter physics and quantum field theory. Unfortunately, none of these advances are taught in graduate courses in statistical mechanics. This book is an attempt to correct this problem. It begins with theorems on the existence (and lack) of order for crystals and magnets and with the theory of critical phenomena, and continues by presenting the methods and results of fifty years of analytic and computer computations of phase transitions. It concludes with an extensive presentation of four of the most important of exactly solved problems: the Ising, 8 vertex, hard hexagon and chiral Potts models.1. Basic Principles; 2. Reductionism, Phenomena and Models; 3. Stability, Existence and Uniqueness; 4. Theorems on Order; 5. Critical Phenomena and Scaling Theory; 6. Mayer Virial Expansions and Groenevelt's Theorems; 7. Ree-Hoover Virial Expansion and Hard Spheres; 8. High Density Expansions; 9. High Temperature Expansions for Magnets at H=0; 10. The Ising Model in Two Dimensions; Summary of Results; 11. The Pfaffian Solution of the Ising Model; 12. Ising Model Spontaneous Magnetization, Form Factors and Susceptibility; 13. The Star-Triangle (Yang-Baxter) Equation; 14. The Eight Vertex and XYZ models; 15. The RSOS and the Chiral Potts models; 16. Conclusion
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