Finite-size scalings of the Euclidean $\varphi^4$ model at and above the critical dimension
The study of finite-size scaling in systems at and above their upper critical dimension, particularly concerning the breaking of the hyperscaling relation. For models in the Ising universality class Renormalisation Group (RG) arguments—such as those by Brézin and Zinn-Justin (1978) on the susceptibility profile and the work by Flores-Sola, Berche, Kenna and Weigel (2016) on role of the other Fourier models provided key predictions for this behaviour. In my talk, I will discuss theorems that verify these predictions based on a rigorous RG argument.