Convexity in the Theory of Lattice Gases (eBook)

Robert B. Israel (Autor)

eBook Download: PDF

2015 | 1. Auflage
258 Seiten
Princeton University Press (Verlag)
978-1-4008-6842-1 (ISBN)

Infos

In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "e;pathological,"e; others exhibit more "e;reasonable"e; behavior. As an example, the author considers the isotropic Heisenberg model. Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic.Originally published in 1979.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Produkt-Details

• Erscheint lt. Verlag: 8.3.2015
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Series in Physics
• Reihe/Serie: Princeton Series in Physics
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Schlagworte: Abelian von Neumann algebra • Antiisomorphism • Banach space • Blaschke selection theorem • Boundary value problem • Bounded set (topological vector space) • Characteristic function (probability theory) • Choquet theory • commutative property • concave function • Configuration space • Continuous function (set theory) • convex combination • Convex cone • convex function • convex hull • convex set • Correlation function • Correlation function (quantum field theory) • Degrees of freedom (statistics) • Density Matrix • Diagram (category theory) • Difference quotient • Differentiable function • Dimension (vector space) • Dirac delta function • Distribution (mathematics) • Enthalpy • Equation • Equation of State • Ergodicity • Expectation value (quantum mechanics) • Extreme point • ferromagnetism • gases • Hausdorff dimension • Hausdorff measure • Heisenberg model (quantum) • Hölder's inequality • Hyperbolic function • Inclusion–exclusion principle • Inequality (mathematics) • Infimum and supremum • integral equation • Ising Model • KMS state • laws of thermodynamics • Lebesgue measure • Limit point • linear equation • Liouville's theorem (complex analysis) • Lipschitz continuity • Locally convex topological vector space • Mean field theory • Metric Space • Minimum phase • Morera's theorem • Naturalness (physics) • non-equilibrium thermodynamics • Norm (mathematics) • Orthonormal basis • Partition function (statistical mechanics) • Phase diagram • phase rule • Phase space • phase transition • Positive and negative parts • Probability • Probability Distribution • probability measure • product measure • Product topology • Proportionality (mathematics) • quantum statistical mechanics • quantum system • Radon–Nikodym theorem • Riesz representation theorem • Scalar (physics) • second law of thermodynamics • Self-adjoint • Set (mathematics) • Statistical Mechanics • Stone–Weierstrass theorem • subadditivity • Subset • symmetry breaking • Tangent Space • Theorem • theory • Thermodynamic Equilibrium • Thermodynamic Limit • thermodynamics • Thermodynamic system • Thermodynamic Temperature • two-dimensional space • Unit sphere • Vapor • Variational inequality • Variational Principle • Weak operator topology
• ISBN-10: 1-4008-6842-4 / 1400868424
• ISBN-13: 978-1-4008-6842-1 / 9781400868421