Logarithmic Singularities of Specific Heat and Related Properties of Liquid $^4He$ Near $\lambda-$Point

TL;DR

This paper investigates the logarithmic singularity of specific heat and related properties of liquid helium-4 near the lambda point, confirming the intrinsic logarithmic nature through microscopic theory and experimental agreement.

Contribution

It provides the first microscopic theoretical confirmation that the singularity of specific heat at the lambda point is logarithmic, supported by experimental data.

Findings

Logarithmic singularity of specific heat confirmed by microscopic theory.

Good agreement between theoretical predictions and experimental results.

Weak effects like gravity and sample size influence the observed singularity.

Abstract

The singularity of specific heat ($C_p$) and related properties (viz. thermal expansion coefficient, compressibility and pressure coefficient) of liquid $^4He$ at $\lambda-$point is studied and the accuracy of its logarithmic nature as concluded for the first time from a microscopic theory (cond-mat/0606571) of a system of interacting bosons is examined. A very good agreement between the results of this theory and experiments concludes that singularity is intrinsically logarithmic. However, as shown by other studies, weak effects arising from earth's gravity and small sample size round it off and $C_p$ assumes asymptotic nature near $T_{\lambda}$.