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

Format:

Book

Author/Creator:

Brankov, Iordan.

Contributor:

Danchev, Daniel M.

Tonchev, Nicholai S.

Series:

Series in Modern Condensed Matter Physics

Series in modern condensed matter physics ; vol. 9

Language:

English

Subjects (All):

Critical phenomena (Physics).

Finite size scaling (Physics).

Physical Description:

1 online resource (459 p.)

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2000.

Language Note:

English

Summary:

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

Contents:

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

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

6.1 Introduction

Notes:

Description based upon print version of record.

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

ISBN:

9789812813435

9812813438