Application of Minimal Subtraction Renormalization to Crossover Behavior near the $^3$He Liquid-Vapor Critical Point

TL;DR

This paper applies minimal subtraction renormalization within the $$He liquid-vapor critical point to model crossover behavior of thermodynamic properties, fitting experimental data with a unified theoretical approach.

Contribution

It introduces a parametric scheme based on minimal subtraction renormalization to accurately describe crossover behavior near the critical point of $^3$He.

Findings

Good agreement with experimental data within |t| ≤ 2×10^{-2}

Unified theoretical expressions fit susceptibility and heat capacity data

Effective modeling of crossover behavior in $^3$He near criticality

Abstract

Parametric expressions are used to calculate the isothermal susceptibility, specific heat, order parameter, and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region. These expressions are based on the minimal-subtraction renormalization scheme within the $\phi^4$ model. Using two adjustable parameters in these expressions, we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and early measurements of coexistence curve and light scattering intensity along the critical isochore of $^3$He near its liquid-vapor critical point. The theory provides good agreement with these experimental measurements within the reduced temperature range $|t| \le 2\times 10^{-2}$.