Statistical Mechanics of LiquidHe4

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 long-range permutations as well as nearest-neighbor permutations (to which the previous analysis by one of the authors was restricted). The result indicates a second-order phase transition at the X point. The marked improvements over the previous treatment are:(1) the specific heat behaves as T s near absolute zero, (2) the specific heat peak is more pronounced at the X point, and (3) when triangles are added as possible finite polygons above T\ the specific heat just above T\ increases over the previous result, showing an improvement. Equating the theoretical X point with the experimental, a value for the effective mass of a helium atom about 1.6 times the normal mass is obtained.

Physics of strongly coupled quark–gluon plasma

“…Feynman estimated that he expected the critical value to be in the range y c = 1/4 -1/3. Kikuchi et al [127] have argued that the critical action should be S c ≈ 1.9, but later studies in the eighties such as by Elser [129] determined numerically that the critical action is smaller S c ≈ 1.44.…”

Bose-Einstein condensation of strongly interacting bosons: From liquidHe4to QCD monopoles

“…Otherwise, using the physical Helium mass we obtain T c = 3.57 which is, of course 64% bigger than the real critical temperature. In the eighties Elser [3] determined numerically that the critical action should be smaller than the values obtained in [4], S c ≈ 1.44. Using this new parameter the predicted critical temperature reduces to T c = 2.72, closest to the physical temperature.…”

“…Feynman mentioned that he expected y c = 1/4 -1/3. The combinatoric problem to find the correct critical value of the Feynman parameter, was studied in details by Kikuchi et al [4]. They found a critical action S c ≈ 1.9.…”

Finite Cycle Gibbs Measures on Permutations of $${{\mathbb Z}^d}$$ Z d

“…The Feynman-Kac representation of the Bose gas consists of trajectories of interacting Brownian motions in a fixed time interval, which start and finish at the points of a spatial point process [5] . In order to attempt a rigorous analysis of the model, several simplifications have been proposed over the years [5,6,12,13]. In the resulting model, the starting and ending points belong to the d-dimensional lattice, and the interaction is reduced to an exclusion condition on the paths at the beginning and the end of the time interval.…”