Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Tanja Pasurek
Universität Bielefeld
Gibbs states of disordered anharmonic crystals
We consider a multi-component continuum model of classical particles described by their positions x ∈ R n
and vector spins sx ∈ R m . The interaction between the particles is given by the pair potential
W(x,y;sx,sy) := φ (|x − y|R n) + J (|x − y|R n) · |sx − sy| 2 R m, x,y ∈ Rn .
The purely position term φ (|x − y|Rn) is assumed to be superstable (e.g., of the Lennard-Jones type). The
intensity J (|x − y|Rn) of the harmonic spin-spin interactions |sx − sy| 2 Rm is bounded and of finite range, but
not necessary ferromagnetic. The reference (i.e., free) measure is the Poisson point process πσ on the
marked configuration space Γ(Rn ,Rm ) with the intensity measure σ(dx,ds) = exp{−V (s)}dxds, where
V (s) is an anharmonic single-spin potential. We construct corresponding Gibbs distributions both in the
annealed and quenched approaches and discuss their properties.
Anatoly Vershik
t.b.a.
t.b.a.
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