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Phase transitions for dilute particle systems with potentials of Lennard-Jones type

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We consider a dilute stationary system of N particles uniformly distributed in space and interacting pairwise according to a compactly supported potential, which is repellent at short distances and attractive at moderate distances. We are interested in the large-N behaviour of the system. We show that at a certain scale there are phase transitions in the temperature parameter and describe the energy and ground states explicitly in terms of a variational problem. This is a joint work with Andrea Collevecchio, Wolfgang Koenig and Peter Moerters.

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