Glassy states: the free Ising model on a tree
Daniel GandolfoCPT - Centre de Physique Théorique - UMR 7332 (Centre de Physique Théorique
Campus de Luminy, Case 907
163 Avenue de Luminy
13288 Marseille cedex 9, France - France)Christian MaesInstituut voor Theoretische Fysica (Institute for Theoretical Physics, K.U.Leuven Celestijnenlaan 200D B-3001 Leuven - Belgium)Jean RuizCPT - Centre de Physique Théorique - UMR 7332 (Centre de Physique Théorique
Campus de Luminy, Case 907
163 Avenue de Luminy
13288 Marseille cedex 9, France - France)Senya ShlosmanCPT - Centre de Physique Théorique - UMR 7332 (Centre de Physique Théorique
Campus de Luminy, Case 907
163 Avenue de Luminy
13288 Marseille cedex 9, France - France)
2017en
ABI
Аннотация
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) magnetization obtained from drawing boundary conditions from the free state.
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