Universal scaling in non-integer dimensions
Prof. Nicolò Defenu (ETH Zürich)

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. The seminar introduces a definition of universal scaling on a non-homogeneous graph. The corresponding scaling theory is expected to depend only on a single parameter, the spectral dimension ds, which plays the role of the relevant parameter on complex geometries. We will then focus on a concrete example, the long-range diluted graph (LRDG), which allows to tune the value of the spectral dimension continuously. By means of extensive numerical simulations, we probe the scaling exponents of a simple instance of O(N) symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in fractional dimensions.