Fundamentals of statistical physics: the lectures - a survey one particle and many Gaussian distributions quantum mechanics and lattices. Random dynamics: diffusion and hopping from hops to statistical mechanics correlations and response. More statistical mechanics: statistical thermodynamics Fermi, Bose, and other. Phase transitions: overview of phase transitions mean field theory of critical behaviour continuous phase transitions renormalization in one dimension real space renormalization techniques duality planar model and Coulomb systems XY model, renormalization and duality.
Fundamentals of statistical physics: the lectures - a survey one particle and many Gaussian distributions quantum mechanics and lattices. Random dynamics: diffusion and hopping from hops to statistical mechanics correlations and response. More statistical mechanics: statistical thermodynamics Fermi, Bose, and other. Phase transitions: overview of phase transitions mean field theory of critical behaviour continuous phase transitions renormalization in one dimension real space renormalization techniques duality planar model and Coulomb systems XY model, renormalization and duality.
The sophistication of modern tools used in the study of statistical mechanics and field theory is often an obstacle to the easy understanding of new important current results reported in journals. The main purpose of this book is to introduce the reader to the methods of the fluctuation (field) theory of phase transitions and critical phenomena so as to provide a good source for research. The introductory contents are concerned with ideas of description, thermodynamic stability theory related to phase transitions, major experimental facts, basic models and their relationships. Special attention is paid to the mean field approximation and to the Landau expansion for simple and complex models of critical and multicritical phenomena. An instructive representation of the modern perturbation theory and the method of the renormalization group is developed for field models of phase transitions. The essential influence of the fluctuations on the critical behaviour is established together with the theory of correlation functions, Gaussian approximation, the Ginzburg criterion, [symbol]- and 1/n- expansions as practical realizations of the renormalization group ideas. Applications of the theory to concrete aspects of condensed matter physics are considered: quantum effects, Bose condensation, crystal anisotropy, superconductors and liquid crystals, effects of disorder of type randomly distributed quenched impurities and random fields. This volume can be used as an advanced University course book for students with a basic knowledge of statistical physics and quantum mechanics. It could be considered as a complementary text to a standard University course on statistical physics
Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm–Pines and Chern–Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.
1. Quantum Field Theory and Renormalization Group 2. Gaussian Expectation Values. Steepest Descent Method . 3. Universality and Continuum Limit 4. Classical Statistical Physics: One Dimension 5. Continuum Limit and Path Integral 6. Ferromagnetic Systems. Correlations 7. Phase transitions: Generalities and Examples 8. Quasi-Gaussian Approximation: Universality, Critical Dimension 9. Renormalization Group: General Formulation 10. Perturbative Renormalization Group: Explicit Calculations 11. Renormalization group: N-component fields 12. Statistical Field Theory: Perturbative Expansion 13. The sigma4 Field Theory near Dimension 4 14. The O(N) Symmetric (phi2)2 Field Theory: Large N Limit 15. The Non-Linear sigma-Model 16. Functional Renormalization Group Appendix 1. Quantum Field Theory and Renormalization Group 2. Gaussian Expectation Values. Steepest Descent Method . 3. Universality and Continuum Limit 4. Classical Statistical Physics: One Dimension 5. Continuum Limit and Path Integral 6. Ferromagnetic Systems. Correlations 7. Phase transitions: Generalities and Examples 8. Quasi-Gaussian Approximation: Universality, Critical Dimension 9. Renormalization Group: General Formulation 10. Perturbative Renormalization Group: Explicit Calculations 11. Renormalization group: N-component fields 12. Statistical Field Theory: Perturbative Expansion 13. The sigma4 Field Theory near Dimension 4 14. The O(N) Symmetric (phi2)2 Field Theory: Large N Limit 15. The Non-Linear sigma-Model 16. Functional Renormalization Group Appendix
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behaviour, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among other applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.
These lectures describe the physics of phase transitions and critical phenomena. After introducing the thermodynamics of phase transitions, these general considerations are made explicit by presenting statistical mechanical calculations on a lattice gas model in the mean-field approximation. Then the Landau theory of phase transitions is presented. The form of free energy in the Landau theory is motivated by an explicit mean field calculation for the Ising model. This is followed by a discussion of spatial correlations and the breakdown of the mean field theory due to increase of spatial fluctuations near the critical point. This calculation also brings out the role of dimension of the system for the critical behaviour. The basic ideas of Renormalization Group (RG) are then introduced and illustrated by a simple RG calculation for the one-dimensional Ising model. Real-space RG calculations are then applied to the two-dimensional Ising model on the triangular lattice, which, in fact, brings forth several key features of the RG technique. A discussion of more general aspects of the RG formalism, such as scaling for spatial correlation functions, relevant and irrelevant couplings, universality, upper critical dimension, etc. are introduced.
Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm-Pines and Chern-Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.