- 02-519 Christof Kuelske
- Regularity properties of potentials for
joint measures of random spin systems
Dec 15, 02
(auto. generated ps),
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Abstract. We consider general quenched disordered lattice spin models on
compact local spin spaces with possibly dependent disorder. We
discuss their corresponding joint measures on the product space
of disorder variables and spin variables in the infinite volume.
These measures often possess pathologies in a low temperature region
reminiscent of renormalization group pathologies in the sense that
they are not Gibbs measures on the product space. Often the joint
measures are not even almost Gibbs, but it is known that there is
always a potential for their conditional expectations that may
however only be summable on a full measures set, and not everywhere.
In this note we complement the picture from the non-pathological side.
We show regularity properties for the potential in the region of
interactions where the joint potential is absolutely summable
We prove unicity and Lipschitz-continuity, much in analogy to the
two fundamental regularity theorems proved by van Enter, Fernandez,
Sokal for renormalization group transformations.