%0 Journal Article
%T Gibbs states of lattice spin systems with unbounded disorder
%A Yu. Kondratiev
%A Yu. Kozitsky
%A T. Pasurek
%J Condensed Matter Physics
%D 2010
%I Institute for Condensed Matter Physics
%X The Gibbs states of a spin system on the lattice Zd with pair interactions Jxy¦Ò(x) ¦Ò(y) are studied. Here ¡Ê E, i.e. x and y are neighbors in Zd. The intensities Jxy and the spins ¦Ò(x), ¦Ò(y) are arbitrarily real. To control their growth we introduce appropriate sets Jq RE and Sp RZd and show that, for every J = (Jxy)¡ÊJq: (a) the set of Gibbs states Gp(J) = {¦Ì: solves DLR, ¦Ì(Sp) = 1} is non-void and weakly compact; (b) each ¦Ì¡ÊGp(J) obeys an integrability estimate, the same for all ¦Ì. Next we study the case where Jq is equipped with a norm, with the Borel ¦Ò-field B(Jq), and with a complete probability measure ¦Í. We show that the set-valued map Jq J ¡ú Gp(J) has measurable selections Jq J ¡ú ¦Ì(J) ¡ÊGp(J), which are random Gibbs measures. We demonstrate that the empirical distributions N-1¦²n=1N¦Ð¦¤n(¡¤|J,¦Î), obtained from the local conditional Gibbs measures ¦Ð¦¤n(¡¤|J,¦Î) and from exhausting sequences of ¦¤n Zd, have ¦Í-a.s. weak limits as N¡ú+¡Þ, which are random Gibbs measures. Similarly, we show the existence of the ¦Í-a.s. weak limits of the empirical metastates N-1¦²n=1N¦Ä¦Ð¦¤n(¡¤|J,¦Î), which are Aizenman-Wehr metastates. Finally, we demonstrate that the limiting thermodynamic pressure exists under some further conditions on ¦Í.
%K Aizenman-Wehr metastate
%K Newman-Stein empirical metastate
%K chaotic size dependence
%K Komlo's theorem
%K quenched pressure
%K spin glass
%U http://dx.doi.org/10.5488/CMP.13.43601