Critical behavior in finite systems:: The superfluid transition of 4He in a confined geometry.

An important problem in thermodynamics and statistical mechanics is the way a finite system approaches the thermodynamic limit. This problem is even more acute in systems near a second order phase transition. In this case there is a length scale, the correlation length, which diverges as the transition is approached. The expectation, according to finite-size correlation length scaling, is that such finite systems, when measured under suitable conditions, should be rescaled in a way which involves only the critical properties of the same system as realized in the thermodynamic limit. We report measurements of the specific heat of confined helium near the superfluid transition. These data agree with correlation-length scaling over some temperature range, but disagree in the region where the helium becomes superfluid. This rather unexpected result remains unexplained and needs further experiments to be fully understood.