Comparison of the Critical Properties of the S = 1/2 XY Model and Liquid Helium Near the Lambda Transition

Abstract

Experimental properties of the lambda line of liquid helium are used together with properties of the zero-field spin 1/2 XY model to determine, on the one hand, the point on the lambda line to which the zero-field model applies, and on the other hand, to determine the lattice spacing of the model. On the f.c.c. lattice the specific heat of the model, C/NkB ~ −0.255 ln (1 − Tc/T) − 0.190 near Tc. This result is shown to be in good agreement with recent experimental results of Ahlers on liquid helium. Other properties of the S = 1/2 XY model are also calculated and, where comparison can be made, agree well with experiment.