Gibbs states of lattice spin systems with unbounded disorder

Kondratiev Y, Kozitsky Y, Pasurek T (2010)
CONDENSED MATTER PHYSICS 13(4): 43601.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Gibbs states of a spin system on the lattice Z(d) with pair interactions J(xy)sigma(x)sigma(y) are studied. Here (x, y) is an element of E, i.e. x and y are neighbors in Z(d). The intensities J(xy) and the spins sigma(x), sigma(y) are arbitrarily real. To control their growth we introduce appropriate sets I-q subset of R-E and S-p subset of R-zd and show that, for every J = (J(xy)) is an element of I-q : (a) the set of Gibbs states G(p)(J) = {mu : solves DLR, mu(S-p) = 1} is non-void and weakly compact; (b) each mu is an element of G(p)(J) obeys an integrability estimate, the same for all mu. Next we study the case where I-q is equipped with a norm, with the Borel B(I-q), and with a complete probability measure v. We show that the set-valued map I-q (sic) J bar right arrow G(p) (J) has measurable selections I-q (sic) J bar right arrow mu(J) is an element of G(p)(J), which are random Gibbs measures. We demonstrate that the empirical distributions N-1 Sigma(N)(n=1) pi(Delta n) (.vertical bar J,xi), obtained from the local conditional Gibbs measures pi(Delta n) (.vertical bar J,xi) and from exhausting sequences of Delta(n) subset of Z(d), have v-a.s, weak limits as N -> +infinity, which are random Gibbs measures. Similarly, we show the existence of the v-a.s, weak limits of the empirical metastates N-1 Sigma(N)(n=1) (delta)pi(Delta n) (.vertical bar J,xi), which are Aizenman-Wehr metastates. Finally, we demonstrate that the limiting thermodynamic pressure exists under some further conditions on v.
Stichworte
spin glass; quenched pressure; Newman-Stein empirical metastate; Aizenman-Wehr metastate; chaotic size; Komlos theorem; dependence
Erscheinungsjahr
2010
Zeitschriftentitel
CONDENSED MATTER PHYSICS
Band
13
Ausgabe
4
Art.-Nr.
43601
ISSN
1607-324X
Page URI
https://pub.uni-bielefeld.de/record/2003435

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Kondratiev Y, Kozitsky Y, Pasurek T. Gibbs states of lattice spin systems with unbounded disorder. CONDENSED MATTER PHYSICS. 2010;13(4): 43601.
Kondratiev, Y., Kozitsky, Y., & Pasurek, T. (2010). Gibbs states of lattice spin systems with unbounded disorder. CONDENSED MATTER PHYSICS, 13(4), 43601
Kondratiev, Y., Kozitsky, Y., and Pasurek, T. (2010). Gibbs states of lattice spin systems with unbounded disorder. CONDENSED MATTER PHYSICS 13: 43601.
Kondratiev, Y., Kozitsky, Y., & Pasurek, T., 2010. Gibbs states of lattice spin systems with unbounded disorder. CONDENSED MATTER PHYSICS, 13(4): 43601.
Y. Kondratiev, Y. Kozitsky, and T. Pasurek, “Gibbs states of lattice spin systems with unbounded disorder”, CONDENSED MATTER PHYSICS, vol. 13, 2010, : 43601.
Kondratiev, Y., Kozitsky, Y., Pasurek, T.: Gibbs states of lattice spin systems with unbounded disorder. CONDENSED MATTER PHYSICS. 13, : 43601 (2010).
Kondratiev, Yuri, Kozitsky, Yu., and Pasurek, Tatiana. “Gibbs states of lattice spin systems with unbounded disorder”. CONDENSED MATTER PHYSICS 13.4 (2010): 43601.

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