Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric φ^4 model in three dimensions below T_c

Details Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric φ^4 model in three dimensions below T_c Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric φ^4 model in three dimensions below T_c

1998-06-08

arxiv.org/abs/cond-mat/9806103v2

Nucl.Phys. B540 (1999) 654-678

Physics

Condensed Matter

Statistical Mechanics

29 pages LaTeX including 3 PostScript figures, to appear in Nucl. Phys. B [FS] (1998)

Scientific paper

10.1016/S0550-3213(98)00699-3

We present an analytic three-loop calculation for thermodynamic quantities of the O(n) symmetric \phi^4 theory below T_c within the minimal subtraction scheme at fixed dimension d=3. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the three-loop terms of the amplitude functions f_phi, F+ and F- of the order parameter and the specific heat above and below T_c, respectively, without using the \epsilon=4-d expansion. A Borel resummation for the case n=2 yields resummed amplitude functions f_phi and F- that are slightly larger than the one-loop results. Accurate knowledge of these functions is needed for testing the renormalization-group prediction of critical-point universality along the \lambda-line of superfluid He(4). Combining the three-loop result for F- with a recent five-loop calculation of the additive renormalization constant of the specific heat yields excellent agreement between the calculated and measured universal amplitude ratio A+/A- of the specific heat of He(4). In addition we use our result for f_phi to calculate the universal combination R_C of the amplitudes of the order parameter, the susceptibility and the specific heat for n=2 and n=3. Our Borel-resummed three-loop result for R_C is significantly more accurate than the previous result obtained from the \epsilon-expansion up to O(\epsilon^2).

Affiliated with

Also associated with

No associations

Rating

Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric φ^4 model in three dimensions below T_c does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric φ^4 model in three dimensions below T_c, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric φ^4 model in three dimensions below T_c will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-412546