Principles of equilibrium statistical mechanics (Q2707389)

The 3 parts (13 chapters) of the book are devoted to reviewing the fundamental principles of equilibrium statistical mechanics. General principles of the thermodynamics of ideal, real gases, including phase transition phenomena, are analyzed in the first part (two chapters). The authors prefer to use the term ``thermostatic'' instead of the commonly used term ``thermodynamic'' trying to underline that they are only describing the theory of equilibrium states. The basic principles of equilibrium statistical mechanics: closed and open classical systems, the maximum entropy principle, quantum systems, fluctuations, correlations and response are discussed in the second part of the book.NEWLINENEWLINENEWLINEThe main part of this book (7 chapters) is devoted to the statistical mechanics of interacting systems. The aim of this part is to give the most commonly used approaches for modeling interacting systems. In Chapter 7, the thermodynamic limit of interacting systems for some simple models is discussed. The exact solution of the one-dimensional Ising model is presented. The approaches that are developed for \(n\)-dimensional Ising models are shortly discussed. Computational simulations based on Monte Carlo and molecular dynamics methods are introduced in Chapter 9. Here the basic principles of numerical calculation are only discussed.NEWLINENEWLINENEWLINETwo mean-field approaches (the first mean-field theory that is based on the microscopic Hamiltonian helps finding an approximate solution of the problem, the second alternative approach is based on a semi-phenomenological free-energy-like expression and takes into account the symmetric properties of investigated systems) are presented in Chapters 10-12.NEWLINENEWLINENEWLINEThe last Chapter 13 gives a short review of general aspects of scaling and renormalization group theories. A short mathematical appendix concludes the book.NEWLINENEWLINENEWLINEUnfortunately, any kind comparison of the macroscopic results with the microscopic approaches, and numerical simulation is not done. This book may be useful for advanced graduate students and for scientists who are working in other fields of physics and mechanics.