Math Physics Seminar, Alessandro Giuliani, University of Rome, Striped states at the ferromagnetic transition
We consider a two-dimensional Ising model with nearest neighbor ferromagnetic and long-range, power-law decaying, antiferromagnetic interactions. We assume that the decay exponent of the antiferromagnetic part is larger than 4. The ground state displays a transition as the strength of the ferromagnetic interaction J is increased: if J is smaller than a critical value J_c, then the ground state is non-uniform, while it becomes uniform for all J>J_c. The transition to the uniform state is believed to take place in a ``universal" manner, via a sequence of transitions among periodic striped states. In this talk we report recent rigorous results confirming this picture: namely, the ratio of the ground state energy to the one of the optimal periodic striped state tends to 1 as J-->J_c^-. The proof is based on a combination of localization bounds into mesoscopic boxes and reflection positivity. Joint work with E. Lieb and R. Seiringer.
Location: Jadwin A06
Date/Time: 05/07/13 at 4:30 pm - 05/07/13 at 6:00 pm
Category: Mathematical Physics Seminar