Statistical Mechanics

Selecta of Elliott H. Lieb

By: Bruno Nachtergaele (Editor), E.H. Lieb, Jan Philip Solovej (Editor)

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Hardcover | 29 November 2004

At a Glance

Hardcover
520 Pages

Edition Type
Annotated

Dimensions(cm)
23.5 x 16.51 x 2.54

Hardcover

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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 physicist 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.

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Existence of thermodynamics for real matter with Coulomb forces	p. 13
The constitution of matter : existence of thermodynamics for systems composed of electrons and nuclei	p. 17
Suppression at high temperature of effects due to statistics in the second virial coefficient of a real gas	p. 27
Calculation of exchange second virial coefficient of a hard-sphere gas by path integrals	p. 29
Monomers and dimers	p. 41
Theory of monomer-dimer systems	p. 45
A property of zeros of the partition function for Ising spin systems	p. 89
A general Lee-Yang theorem for one-component and multicomponent ferromagnets	p. 93
Existence of phase transitions for anisotropic Heisenberg models	p. 123
Phase transitions in anisotropic lattice spin systems	p. 127
Phase transitions in quantum spin systems with isotropic and nonisotropic interactions	p. 163
Phase transitions and refection positivity, I : general theory and long range lattice models	p. 213
Phase transitions and reflection positivity, II : lattice systems with short-range and Coulomb interactions	p. 247
Lattice models for liquid crystals	p. 299
Existence of Neel order in some spin-1/2 Heisenberg antiferromagnets	p. 315
The X Y model has long-range order for all spins and all dimensions greater than one	p. 327
The third law of thermodynamics and the degeneracy of the ground state for lattice systems	p. 333
A guide to entropy and the second law of thermodynamics	p. 353
A fresh look at entropy and the second law of thermodynamics	p. 365
Properties of a harmonic crystal in a stationary nonequilibrium state	p. 373
The statistical mechanics of anharmonic lattices	p. 379
Time evolution of infinite anharmonic systems	p. 391
Lattice systems with a continuous symmetry III : low temperature asymptotic expansion for the plane rotator model	p. 401
The finite group velocity of quantum spin systems	p. 425
The classical limit of quantum of spin systems	p. 433
A refinement of Simon's correlation inequality	p. 447
Fluxes, Laplacians, and Kasteleyn's theorem	p. 457
Selecta of Elliott H. Lieb	p. 485
Publications of Elliott H. Lieb	p. 487
Table of Contents provided by Blackwell. All Rights Reserved.

Statistical Mechanics

Selecta of Elliott H. Lieb

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