The superfluidtransition of 4He, a test case for finite-size scaling at asecond-order phase transition

Abstract

The second-order phase transition of 4He from a normal fluid to asuperfluid is ideally suited for studies of critical behaviour. Inparticular, effects of confinement have been studied recently toverify theoretical predictions of correlation-length scaling andcalculations of specific scaling functions. These predictions aresummarized for the specific heat and the superfluid density. Themethod of achieving confinement is discussed, as well as themeasuring technique. The specific heat and the superfluid densityin planar confinement are examined. It is found that the specificheat scales well on the normal side, and just as well on thesuperfluid side until the region of the specific heat maximum isreached. Here deviations from scaling are seen. It is possiblethat this behaviour is associated with the specific crossover in twodimensions. The superfluid fraction, which has been measured forthe same type of confinement in two different ways, does not scale.Results of a calculation for the superfluid density to assess therole of the inhomogeneity induced by the van der Waals attraction atthe confining walls are presented.