05.07.2018 14:30 Johannes Bäumler (TUM):
Uniqueness and non uniqueness for spin-glass ground states on treesBC1 2.01.10 (8101.02.110) (Parkring 11, 85748 Garching-Hochbrück)
We consider a Spin Glass at temperature T = 0 with gaussian couplings, where the underlying graph is a locally finite tree. We prove that uniqueness of ground state pairs is equivalent to recurrence of the simple random walk on the tree. Furthermore we give a sufficient condition for the above statements.