Renato Calleja, Rafael de la Llave
Computation of the breakdown of analyticity in statistical mechanics models
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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.