Theory of Critical Phenomena in Finite-Size Systems : Scaling and Quantum Effects


Jordan G. Brankov
Bok Engelsk 2000 · Electronic books.
Annen tittel
Utgitt
Singapore : : World Scientific Publishing Company, , 2000.
Omfang
1 online resource (459 p.)
Opplysninger
Description based upon print version of record.. - Contents; Preface; Chapter 1 Overview of Critical Phenomena in Bulk Systems; 1.1 Preliminaries; 1.2 Principles of Statistical Mechanics; Classical continuous systems; Quantum continuous systems; Classical lattice systems; Quantum lattice systems; Statistical definition of thermodynamic functions; 1.3 Thermodynamic limit; 1.4 Equivalence of Gibbs ensembles; 1.5 Phase transitions; 1.5.1 Order parameter; 1.5.2 Critical exponents; 1.5.3 The Landau theory; 1.5.4 Universality and scaling laws; 1.6 Basic facts from the renormalization group theory; 1.6.1 The Ginsburg-Landau model. - 1.6.2 The Gaussian approximation1.6.3 Perturbation expansion; 1.6.4 The Renonormalization Group: Generalities; 1.6.5 Scaling variables and critical exponents; Chapter 2 The Approximating Hamiltonian Method; 2.1 Background ideas; 2.2 Systems with separable attraction; The Bardeen-Cooper-Schrieffer model; Absolute minimum principle; Majorization technique; Extension of the model; Existence of the thermodynamic limit; 2.3 Systems with separable repulsion; Absolute maximum principle; Extension of the model; Existence of the thermodynamic limit; 2.4 Generalization to other types of systems. - 2.4.1 Systems with attractive and repulsive components2.4.2 Systems with nonpolynomial interaction; 2.4.3 Systems of matter interacting with Boson fields; 2.5 Asymptotic closeness of average values; Chapter 3 Exactly Solved Models; 3.1 Classical spherical models; 3.1.1 The spherical and mean spherical models; 3.1.2 Critical behavior of the spherical models; 3.1.3 Equivalent-neighbors spherical models; 3.2 The classical n-vector model and its n → ∞ limit; 3.3 Quantum spherical models; 3.4 Reduced Q4 model; 3.4.1 Model and Approximating Hamiltonians; 3.4.2 Order parameter and critical exponents. - 3.4.3 Some generalizations3.4.4 Long-range order and the r-problem; Chapter 4 Finite-Size Scaling at Criticality; 4.1 Finite-size systems and critical phenomena; 4.2 Phenomenological finite-size scaling; 4.3 Privman-Fisher hypothesis for the free energy; 4.4 Definitions of correlation length; 4.4.1 Bulk correlation length; 4.4.2 Finite-size correlation length; 4.5 Basic hypotheses; 4.5.1 Hypothesis A; 4.5.2 Hypothesis B; 4.6 Extension to several scaling fields; 4.7 Testing finite-size scaling by the spherical models; 4.7.1 General finite-size expressions; 4.7.2 Leading finite-size behavior. - 4.7.3 Finite-size scaling for the correlation function4.7.4 Finite-size scaling for the equation of state; 4.7.5 Finite-size scaling for the free energy density; Chapter 5 Long-Range Interactions; 5.1 Mathematical techniques; 5.2 Finite-size scaling for the correlation function; 5.3 Finite-size scaling for the equation of state; 5.3.1 Finite cube Λ = Ld; 5.3.2 Infinitely long cylinder Λ = Ld-1 x ∞; 5.4 Finite-size shift of the critical temperature; 5.5 Finite-size scaling for the free energy density; 5.6 Crossover to bulk asymptotic behavior; Chapter 6 Modified Finite-Size Scaling. - 6.1 Introduction. - 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
Emner
Sjanger
Dewey
ISBN
9810239254

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