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Statistical Mechanics : Selecta of Elliott H. Lieb

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概要 In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical phys...icist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors.続きを見る
目次 Commentaries
A Survey by the Editors
I. Thermodynamic Limit for Coulomb Systems
I. 1 Existence of Thermodynamics for Real Matter with Coulomb Forces
I. 2 The Constitution of Matter: Existence of Thermodynamics for Systems Composed of Electrons and Nuclei
II. Hard Sphere Virial Coefficients
II. 1 Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas
II. 2 Calculation of Exchange Second Virial Coefficient of a Hard-Sphere Gas by Path Integrals
III. Zeros of Partition Functions
III. 1 Monomers and Dimers
III. 2 Theory of Monomer-Dimer Systems
III. 3 A Property of Zeros of the Partition Function for Ising Spin Systems
III. 4 A General Lee-Yang Theorem for One-Component and Multicomponent Ferromagnets
IV. Reflection Positivity
IV. 1 Existence of Phase Transitions for Anisotropic Heisenberg Models
IV. 2 Phase Transitions in Anisotropic Lattice Spin Systems
IV. 3 Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions
IV. 4 Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models
IV. 5 Phase Transitions and Reflection Positivity. II. Lattice Systems with Short-Range and Coulomb Interactions
IV. 6 Lattice Models for Liquid Crystals
IV. 7 Existence of Néel Order in Some Spin-1/2 Heisenberg Antiferromagnets
IV. 8 The XY Model Has Long-Range Order for all Spins and all Dimensions Greater than One
V. Classical Thermodynamics
V. 1 The Third Law of Thermodynamics and the Degeneracy of the Ground State for Lattice Systems
V. 2 A Guide to Entropy and the Second Law of Thermodynamics
V. 3 A Fresh Look at Entropy and the Second Law of Thermodynamics
VI. Lattice Systems
VI. 1 Properties of a Harmonic Crystal in a Stationary Nonequilibrium State
VI. 2 The Statistical Mechanics of Anharmonic Lattices
VI. 3 Time Evolution of Infinite Anharmonic Systems
VI. 4 Lattice Systems with a Continuous Symmetry III. Low Temperature Asymptotic Expansion for the Plane Rotator Model
VII. Miscellaneous
VII. 1 The Finite Group Velocity of Quantum Spin Systems
VII. 2 The Classical Limit of Quantum Spin Systems
VII. 3 A Refinement of Simon's Correlation Inequality
VII. 4 Fluxes, Laplacians, and Kasteleyn's Theorem
Selecta of Elliott H. Lieb
Publications of Elliott H. Lieb.
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登録日 2020.06.27
更新日 2020.06.28