Experimental evidence of non-Gaussian fluctuations near a critical point

TL;DR

This study provides experimental evidence that near a critical point, liquid crystal fluctuations follow a non-Gaussian distribution, specifically a generalized Gumbel, highlighting the importance of slow modes and degrees of freedom.

Contribution

The paper demonstrates that fluctuations near a second-order transition in liquid crystals follow a generalized Gumbel distribution, revealing non-Gaussian behavior close to the critical point.

Findings

Fluctuations follow a generalized Gumbel distribution near the critical point.

Gaussian distribution is observed away from the critical point.

The Gumbel parameter relates to the effective degrees of freedom.

Abstract

The orientation fluctuations of the director of a liquid crystal are measured, by a sensitive polarization interferometer, close to the Fr\'eedericksz transition, which is a second order transition driven by an electric field. We show that near the critical value of the field the spatially averaged order parameter has a generalized Gumbel distribution instead of a Gaussian one. The latter is recovered away from the critical point. The relevance of slow modes is pointed out. The parameter of generalized Gumbel is related to the effective number of degrees of freedom.