Glassy states: the free Ising model on a tree

Daniel Gandolfo (1, 2) , Christian Maes (3) , Jean Ruiz (1, 2) , Senya Shlosman (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E5 Physique statistique et systèmes complexes
3 Instituut voor Theoretische Fysica

We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The tail observable showing that the free state is not extremal is related to the Edwards-Anderson parameter, measuring the variance of the (random) magnetiza-tion obtained from drawing boundary conditions from the free state.

Domaines: Mathématiques [math]; Physique mathématique [math-ph]

Daniel Gandolfo, Christian Maes, Jean Ruiz, Senya Shlosman. Glassy states: the free Ising model on a tree. 2017. ⟨hal-01648385v1⟩