Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary $k\geq 2$ we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.Comment: 13 page

Book launch and discussion

Book launch event for Nick Drake: Dreaming England (Reaktion 2013) at the NN Cafe, Number 9 Guildhall Road, Northampton, NN1 1DP, Thursday 3rd October 2013. Author Nathan Wiseman-Trowse talked about and read from his book on the musician Nick Drake. Music was provided by Gregg Cave and Ant Savage and the book's photographer Paul Hillery DJd. The event was publically promoted and around sixty attended