Comment on "Quantum critical paraelectrics and the Casimir effect in time"

Details Comment on "Quantum critical paraelectrics and the Casimir effect in time" Comment on "Quantum critical paraelectrics and the Casimir effect in time"

2009-03-30

arxiv.org/abs/0903.5229v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 2 figures

Scientific paper

At variance with the authors' statement [L. P\'{a}lov\'{a}, P. Chandra and P. Coleman, Phys. Rev. B 79, 075101 (2009)], we show that the behavior of the universal scaling amplitude of the gap function in the phonon dispersion relation as a function of the dimensionality $d$, obtained within a self--consistent one--loop approach, is consistent with some previous analytical results obtained in the framework of the $\epsilon$--expansion in conjunction with the field theoretic renormalization group method [S. Sachdev, Phys. Rev. B 55, 142 (1997)] and the exact calculations corresponding to the spherical limit i.e. infinite number $N$ of the components of the order parameter [H. Chamati. and N. S. Tonchev, J. Phys. A: Math. Gen. 33, 873 (2000)]. Furthermore we determine numerically the behavior of the "temporal" Casimir amplitude as a function of the dimensionality $d$ between the lower and upper critical dimension and found a maximum at $d=2.9144$. This is confirmed via an expansion near the upper dimension $d=3$.

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