3
$\begingroup$

Are there any nice uniqueness results for Gibbs-measures on lattice spin systems (graphs) that does not rely on Dobrushin's method?

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ Could you please detail how Dobrushin's method works? $\endgroup$
    – Leonid Petrov
    Commented Nov 23, 2016 at 12:18
  • 2
    $\begingroup$ For a local specification you have to consider its interdependence matrix. If the norm of the matrix is strictly less than 1, then the local specification is compatible with at most one Gibbs measure. (Contraction argument). This procedure can be found in the Book of Anton Bovier - Statistical Mechanics of Disordered Systems. $\endgroup$
    – Martinus Maximus
    Commented Nov 23, 2016 at 13:08
  • 4
    $\begingroup$ There exist many other approaches to prove uniqueness (via suitable coupling methods, via cluster expansion, etc.). However, they are usually harder to check/implement than Dobrushin's one. What are you looking for? $\endgroup$
    – Yvan Velenik
    Commented Nov 24, 2016 at 8:02

0

Reset to default

You must log in to answer this question.