Universal scaling in fractional dimension

Giacomo Bighin, Tilman Enss, Nicolò Defenu

Published 2022-11-23Version 1

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a first study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension $d_s$, which plays the role of the relevant parameter on complex geometries. The graph under consideration allows us to tune the value of the spectral dimension continuously and find the universal exponents as continuous functions of the dimension. 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.