# Mathematics Colloquia and Seminars

### On a model with simultaneous first and second order phase transitions.

Mathematical Physics & Probability

 Speaker: Alain Messager, CNRS Luminy Location: 693 Kerr Start time: Fri, Nov 14 2003, 3:10PM

We consider a family of lattice models defined by an Hamiltonian with a continuous symmetry. This model contains as a particular case the model considered previously by Shlosman and Van Enter. We show that a subfamily of our lattice models exhibits a sophisticated behaviour in space dimension two: the model displays at low temperature a second order phase transition, similar to the one found in the rotator model. But in contrast to the rotator model, our model exhibits up to some inverse temperature beta_t a first order phase transition in the bond variables between two phases: the first one is a "bond ordered phase", which means that the nearest neighbor spins are close; the second one is a "bond antiferromagnetic phase" which means that the nearest neighbor spins are close to opposite. In other words our model exhibits at low temperature either a {\it local ferromagnetic order} or a{\it local antiferromagnetic order}, but {\it not the corresponding long range orders.