09-56 Renato Calleja, Rafael de la Llave

Computation of the breakdown of analyticity in statistical mechanics models (291K, PDF) Mar 26, 09

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Abstract. We consider one dimensional systems of particles interacting and seek quasi-periodic equilibrium states. Standard arguments show that if there are continuous families of ground states, the system can have large scale motion, if the family of ground states is discontinuous, the system is pinned down. We show that there are fast and efficient algorithms that can compute all the continuous families of ground states even close to the boundary of analyticity. We also show that the boundary of analyticity can be computed by running the algorithm and monitoring the solution computed. We implemented these algorithms on several models. We found that there are regions where the boundary is smooth and the breakdown satisfies scaling relations. In other regions, the scalings seem to be interrupted and restart again.

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