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On the number of ground states of the Edwards–Anderson spin glass model

Louis-Pierre Arguin, Michael Damron (2014)

Annales de l'I.H.P. Probabilités et statistiques

Ground states of the Edwards–Anderson (EA) spin glass model are studied on infinite graphs with finite degree. Ground states are spin configurations that locally minimize the EA Hamiltonian on each finite set of vertices. A problem with far-reaching consequences in mathematics and physics is to determine the number of ground states for the model on d for any d . This problem can be seen as the spin glass version of determining the number of infinite geodesics in first-passage percolation or the number...

On the small maximal flows in first passage percolation

Marie Théret (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the standard first passage percolation on d : with each edge of the lattice we associate a random capacity. We are interested in the maximal flow through a cylinder in this graph. Under some assumptions Kesten proved in 1987 a law of large numbers for the rescaled flow. Chayes and Chayes established that the large deviations far away below its typical value are of surface order, at least for the Bernoulli percolation and cylinders of certain height. Thanks to another approach we extend...

On the time constant in a dependent first passage percolation model

Julie Scholler (2014)

ESAIM: Probability and Statistics

We pursue the study of a random coloring first passage percolation model introduced by Fontes and Newman. We prove that the asymptotic shape of this first passage percolation model continuously depends on the law of the coloring. The proof uses several couplings, particularly with greedy lattice animals.

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