Statistical Mechanics: Selecta of Elliott H. LiebIn 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. |
Contents
13 | |
in the Second Virial Coefficient of a Real | 27 |
and Multicomponent Ferromagnets with A D Sokal 9335 | 93 |
and Nonisotropic Interactions with F J Dyson and B Simon | 163 |
with J Fröhlich R B Israel and B Simon | 247 |
Antiferromagnets with T Kennedy and S Shastry | 315 |
of the Ground State for Lattice Systems with M Aizenman | 333 |
with J Yngvason | 353 |
VII | 370 |
with O E Lanford and J L Lebowitz | 391 |
W Robinson | 425 |
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Common terms and phrases
a₁ adiabatic adiabatic process anisotropic antiferromagnet arXiv B₁ Barry Simon boundary conditions chessboard estimate classical configuration consider contour convex Coulomb defined definition denote dimensions dimer Dyson E. H. Lieb edge weights eigenvalues Elliott H entropy equilibrium example existence ferromagnetic finite free energy given graph ground H₁ Hamiltonian Heisenberg model implies inequality infrared bounds integral interaction Ising model Jürg Fröhlich Lebowitz Lee-Yang theorem Lemma Lett long-range order lower bound magnetic Math Mathematical matrix method monomer-dimer nearest neighbor Néel order obtain P₁ partition function Peierls argument Phase Transitions Phys Physics plane polynomial proof Proposition prove Quantum Spin Quantum Spin Systems reflection positivity Remark resp result Section simple system square state-space statistical mechanics sublattice symmetry temperature theory thermodynamic limit Transitions and Reflection upper bound vector vertex vertices Yngvason zero αγ