Observables at Infinity and States with Short Range : Correlations in Statistical Mechanics
MECANIQUE STATISTIQUE
FONCTIONS DE CORRELATION
INFORMATIQUE QUANTIQUE
THEORIE DES TREILLIS
Abstract : We say that a representation of an algebra of local observables has short-range correlations if any observable which can be measured outside all bounded sets is a multiple of the identity, and that a state has finite range correlations if the corresponding cyclic representation does. We characterize states with short-range correlations by a cluster property. For classical lattice systems and continuous systems with hard cores, we give a definition of equilibrium state for a specific interaction, based on a local version of the grand canonical prescription; an equilibrium state need not be translation invariant. We show that every equilibrium state has a unique decomposition into equilibrium states with short-range correlations. We use the properties of equilibrium states to prove some negative results about the existence of metastable states. We show that the correlation functions for an equilibrium state satisfy the Kirkwood-Salsburg equations; thus, at low activity, there is only one equilibrium state for a given interaction, temperature, and chemical potential. Finally, we argue heuristically that equilibrium states are invariant under time-evolution.
LANDFORD
RUELLE
P/69/12
IHES
[06/1969]
A4
42 f.
EN
TEXTE
PREPUBLICATION
P_69_12.pdf
1969
Nonsymmetric gravity theories : inconsistencies and a cure
GRAVITATION
RELATIVITE GENERALE
DAMOUR
DESER
MC CARTHY
P/92/36
IHES
06/1992
A4
18 f.
EN
TEXTE
PREPUBLICATION
P_92_36.pdf
1992
Mathematical slices of molecular biology
BIOMATHEMATIQUES
BIOLOGIE MOLECULAIRE
MATHEMATIQUES
GENETIQUE
CYTOLOGIE
GROMOV
CARBONE
M/01/03
IHES
A4
44 f.
EN
TEXTE
PREPUBLICATION
M_01_03.pdf
2001