Network topology transition at criticality

TL;DR

This paper explores how network topology changes at critical points in many-body systems, using network robustness as an indicator to understand phase transitions beyond traditional methods.

Contribution

It introduces a network-based approach to detect critical phenomena in many-body systems, highlighting the transition from homogeneous to heterogeneous network structures.

Findings

Network robustness signals phase transitions.

Homogeneous-heterogeneous transition observed at criticality.

Applicable to 1D quantum and 2D classical XY models.

Abstract

Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by experiments. Therefore we need, beyond mean-field theory, the complex-systems approach that stresses the systemic complexity of many-body network at criticality. According to our previous study, network space experiences the homogeneous-heterogeneous transition invisible in traditional phase transitions. The network robustness can be a useful indicator to capture the critical phenomena of phase transitions with/without symmetry breaking. In this work, we demonstrate the idea of the change of robust networks is successfully applied to the well-known 1D quantum and 2D classical XY models.