Statistical Mechanics of Liquid He^{4}
Abstract
The partition function proposed by Feynman for liquid He^{4}, based on his path integral method, is evaluated for a simple cubic lattice considering longrange permutations as well as nearestneighbor permutations (to which the previous analysis by one of the authors was restricted). The result indicates a secondorder phase transition at the λ point. The marked improvements over the previous treatment are: (1) the specific heat behaves as T^{3} near absolute zero, (2) the specific heat peak is more pronounced at the λ point, and (3) when triangles are added as possible finite polygons above T_{λ} the specific heat just above T_{λ} increases over the previous result, showing an improvement. Equating the theoretical λ point with the experimental, a value for the effective mass of a helium atom about 1.6 times the normal mass is obtained.
 Publication:

Physical Review
 Pub Date:
 September 1960
 DOI:
 10.1103/PhysRev.119.1823
 Bibcode:
 1960PhRv..119.1823K