Bäcklund transformation for the BC-type Toda lattice.
Bipartite mean field spin systems. Existence and solution.
Bounding the partition function of spin-systems.
Bounds on the zeros of a renormalization group fixed point.
Branching processes, and random-cluster measures on trees
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of ‘boundary condition’, namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of random-cluster measures are explored for certain classes of equivalence relations. In proving uniqueness, the following problem concerning branching processes is encountered and answered. Consider bond percolation on the family-tree of a branching process. What is the...