Series in Modern Condensed Matter Physics - Vol. 9
THEORY OF CRITICAL PHENOMENA IN FINITE-SIZE SYSTEMS
Scaling and Quantum Effects
by Jordan G Brankov, Daniel M Danchev (Institute of Mechanics, Bulgarian Academy of Sciences) & Nicholai S Tonchev (G Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences)
The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems.
The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.
Contents:
- Overview of Critical Phenomena in Bulk Systems
- The
Approximating Hamiltonian Method
- Exactly Solved Models
- Finite-Size Scaling at Criticality
- Long-Range Interactions
- Modified Finite-Size Scaling
- Boundary Effects
- Finite-Size Scaling at First Order Transitions
- Limit Gibbs States and Finite-Size Scaling
- Bulk Quantum Systems
- The Casimir Effect
- Survey of Results on the Casimir Effect
Readership: Graduate students and researchers in theoretical and
condensed matter physics.
"... this book offers a careful survey of finite-size scaling near bulk phase transitions ..."
| Journal of Statistical Physics, Jun 2002 |
"The book is a very comprehensive and detailed account of this field ... I have found the final section on the Casimir effect particularly interesting. It is very well written and detailed ... I recommend it to serious students of critical phenomena and condensed matter, but those who already have the basic knowledge of the theory of phase transitions."
| Contemporary Physics, 2002 |
| 460pp |
Pub. date: Aug 2000 |
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