On perturbations of the Ising model

2020/12/25 金 14:00 - 17:00
臼杵 峻亮

It is known that phase transition occurs on the Ising model, that is, there exists $L_c>0$ such that the Ising model has the only one equilibrium state if the inverse temperature parameter $L>0$ satisfies $L<L_c$ and has more than one equilibrium states if $L>L_c$. We perturb the interaction defining the Ising model. Perturbations correspond to some influence from the surroundings to the system or some noise in the interaction. In this talk, we show that the uniqueness of the equilibrium state persists under perturbations for small $L$ and the non-uniqueness also persists under symmetric perturbations of interactions for large $L$.