Control parameter dependence of fluctuation near jamming

TL;DR

This paper investigates how fluctuations near the jamming transition depend on the control parameter, revealing that fluctuations diverge when using the distance to the transition point but not when using pressure.

Contribution

It demonstrates the control parameter dependence of fluctuation divergence near jamming, clarifying the critical behavior in different measurement conditions.

Findings

Fluctuations do not diverge when pressure is the control parameter.

Fluctuations show power-law divergence when the distance to jamming is the control parameter.

The nature of fluctuations depends critically on the choice of control parameter.

Abstract

The fluctuations of the physical quantities play a central role to characterize the critical phenomena. Here, we report that the nature of the fluctuation highly depends on the control parameter near the jamming transition point $\varphi_J$. We show that the fluctuations do not diverge when the pressure is used as the control parameter. On the contrary, if the distance to the transition point $\varphi_J$ is used as the control parameter, the fluctuations show the power-law divergence.