Theory of critical phenomena in finite-size systems : scaling and quantum effects / Jordan G. Brankov, Daniel M. Danchev, Nicholai S. Tonchev.

Includes bibliographical references (pages 415-434) and index.

Overview of Critical Phenomena in Bulk Systems -- Principles of Statistical Mechanics -- Thermodynamic limit -- Equivalence of Gibbs ensembles -- Phase transitions -- Order parameter -- Critical exponents -- The Landau theory -- Universality and scaling laws -- Basic facts from the renormalization group theory -- The Ginsburg-Landau model -- The Gaussian approximation -- Perturbation expansion -- The Renonormalization Group: Generalities -- Scaling variables and critical exponents -- The Approximating Hamiltonian Method -- Systems with separable attraction -- Systems with separable repulsion -- Generalization to other types of systems -- Systems with attractive and repulsive components -- Systems with nonpolynomial interaction -- Systems of matter interacting with Boson fields -- Asymptotic closeness of average values -- Exactly Solved Models -- Classical spherical models -- The spherical and mean spherical models -- Critical behavior of the spherical models -- Equivalent-neighbors spherical models -- The classical n-vector model and its n [right arrow] [infinity] limit -- Quantum spherical models -- Reduced Q[superscript 4] model -- Model and Approximating Hamiltonians -- Order parameter and critical exponents -- Long-range order and the r-problem -- Finite-Size Scaling at Criticality -- Finite-size systems and critical phenomena -- Phenomenological finite-size scaling -- Privman-Fisher hypothesis for the free energy -- Definitions of correlation length -- Bulk correlation length -- Finite-size correlation length.

"The aim of this book is to familiarise the reader with the 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."--Jacket

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