Universal scaling in real dimension

Abstract

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a 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 also to noninteger values and to 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 $O(\mathcal{N})$ symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.

13 pages, 9 figures

References in corpus (10)

• Critical phenomena in complex networks
• Long-range interacting quantum systems
• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Programmable Interactions and Emergent Geometry in an Atomic Array
• On the scaling of the chemical distance in long-range percolation models
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Critical exponents of O(N) models in fractional dimensions
• The correspondence between long-range and short-range spin glasses
• Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

Cited by in corpus (4)

• Optimal spatial searches with long-range tunneling
• Universality of critical dynamics on a complex network
• Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes
• Corrections to scaling in the 2D phi^4 model: Monte Carlo results and some related problems