Master singular behavior from correlation length measurements for seven one-component fluids near their gas-liquid critical point

TL;DR

This paper uncovers a universal master behavior of the correlation length near the gas-liquid critical point for seven one-component fluids, incorporating correction-to-scaling and quantum effects, validated through a scale dilatation method.

Contribution

It introduces a unified description of correlation length behavior near criticality for multiple fluids, including quantum effects, using a scale dilatation approach aligned with renormalization theory.

Findings

Master behavior extends to correction-to-scaling terms

Critical parameter set includes four thermodynamic coordinates and one quantum parameter

Estimates the thermal field extent for critical crossover deviations

Abstract

We present the master (i.e. unique) behavior of the correlation length, as a function of the thermal field along the critical isochore, asymptotically close to the gas-liquid critical point of xenon, krypton, argon, helium 3, sulfur hexafluoride, carbon dioxide and heavy water. It is remarkable that this unicity extends to the correction-to-scaling terms. The critical parameter set which contains all the needed information to reveal the master behavior, is composed of four thermodynamic coordinates of the critical point and one adjustable parameter which accounts for quantum effects in the helium 3 case. We use a scale dilatation method applied to the relevant physical variables of the onecomponent fluid subclass, in analogy with the basic hypothesis of the renormalization theory. This master behavior for the correlation length satisfies hyperscaling. We finally estimate the thermal field extent, where the critical crossover of the singular thermodynamic and correlation functions deviate from the theoretical crossover function obtained from field theory.