Existence and Some Properties of Gibbs Measures in the Continuum

#### Yu.G. Kondratiev, O.V. Kutoviy

2005, v.11, Issue 1, 111-132

ABSTRACT

We develop a modified approach to the study of the existence problem for Gibbs measures of continuous systems with infinite-range pair interactions. We prove the existence of Gibbs measures possessing more a priori properties compared with [R.L. Dobrushin, Gibbsian random fields for particles without hard core, Theor. Math. Fyz., 1970, v.4, 101-118], [E. Pechersky and Yu. Zhukov, Uniqueness of Gibbs state for nonideal gas in $R^d$: The case of pair potentials, J. Stat. Phys., v. 97, 145-172]. A technical advantage of the new proposed approach is that we use appropriate compact functions which come out from the metrical structure of the finite volume configuration space.

Keywords: configuration space,Gibbs measure,existence,specification