Statistical mechanics of quantum spin systems. III |
| |
Authors: | Oscar E. Lanford III Derek W. Robinson |
| |
Affiliation: | (1) I. H. E. S., Bures-sur-Yvette;(2) Department of Mathematics, University of California, Berkeley, California, USA;(3) CERN, Geneva |
| |
Abstract: | In the algebraic formulation the thermodynamic pressure, or free energy, of a spin system is a convex continuous functionP defined on a Banach space of translationally invariant interactions. We prove that each tangent functional to the graph ofP defines a set of translationally invariant thermodynamic expectation values. More precisely each tangent functional defines a translationally invariant state over a suitably chosen algebra of observables, i. e., an equilibrium state. Properties of the set of equilibrium states are analysed and it is shown that they form a dense set in the set of all invariant states over. With suitable restrictions on the interactions, each equilibrium state is invariant under time-translations and satisfies the Kubo-Martin-Schwinger boundary condition. Finally we demonstrate that the mean entropy is invariant under time-translations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|