The lattice phi4 model is a fundamental spin model subject to a quartic potential function. It is believed to be in the same universality class as the O(N) model, and its critical behaviour has been a subject of renormalisation group analysis with small coupling  constant assumption. In dimension 4 or higher, it was observed that the boundary condition plays a crucial role in finite-size scaling at the critical point, but there was a relative lack of work on the principles underlying this phenomenon. In this talk, I will define the hierarchical phi4 model, a toy model for renormalisation group analysis, and show some rigorous results that helps understanding the critical finite-size scaling.
org: GIULIANI Alessandro