%0 Book Section %1 statphys23_0850 %A Cremer, D. %A Dohm, V. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K amplitude borel critical exponents helium lambda ratios statphys23 summation topic-2 transition universal %T Precision results from improved Borel summation of critical exponents and amplitude ratios of the $d=3, n=2$ universality class %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=850 %X Highly accurate experimental results obtained from space experiments near the lambda transition of $^4$He 1 constitute a challenge to analytical renormalization-group (RG) calculations. Theoretical RG predictions with comparatively large error bars have been obtained from previous Borel summations 2. We perform improved Borel summations for the critical exponents $\alpha$ and $\gamma$ of the $d=3, n=2$ universality class on the basis of seven-loop perturbation series of the $\phi^4$ field theory 3 with an $n$ component order parameter in $d$ dimensions. A new extremum criterion is introduced that significantly reduces the error bars compared to the earlier Borel summations 2. Our result for $\alpha=-0.0100.002$ is close to the experimental result $\alpha_exp=-0.0127\pm0.0003$ 1 but disagrees with numerical data for XY type lattice models 4. Furthermore, Borel resummed results on the basis of four-loop perturbation series 5 are presented for the universal amplitude ratios $P=(1-A^+/A^-)/\alpha$ related to the specific heat and for $R_\xi^T$ related to the superfluid density. While our result for $R_\xi^T$ is in good agreement with experiments 6 our result for $P=4.433 0.077$ disagrees with both experimental 1 and numerical results 7. Further theoretical and experimental investigations are required to resolve these discrepancies. 1) J.A. Lipa et al., Phys. Rev. B 68, 174518 (2003) \newline 2) R. Guida, J. Zinn-Justin, J. Phys. A 31, 8103 (1998) \newline 3) D.B. Murray, B.G. Nickel (unpublished) \newline 4) M. Campostrini et al., Phys. Rev. B 74, 14450 (2006) \newline 5) M. Stroesser, V. Dohm, Phys. Rev. E 67, 056115 (2003) \newline 6) A. Singsaas, G. Ahlers, Phys. Rev. B 30, 5103 (1984) \newline 7) M. Hasenbusch, J. Stat Mech. P08019 (2006)

@incollection{statphys23_0850, abstract = {Highly accurate experimental results obtained from space experiments near the lambda transition of $^4$He [1] constitute a challenge to analytical renormalization-group (RG) calculations. Theoretical RG predictions with comparatively large error bars have been obtained from previous Borel summations [2]. We perform improved Borel summations for the critical exponents $\alpha$ and $\gamma$ of the $d=3, n=2$ universality class on the basis of seven-loop perturbation series of the $\phi^4$ field theory [3] with an $n$ component order parameter in $d$ dimensions. A new extremum criterion is introduced that significantly reduces the error bars compared to the earlier Borel summations [2]. Our result for $\alpha=-0.010\pm 0.002$ is close to the experimental result $\alpha_{exp}=-0.0127\pm0.0003$ [1] but disagrees with numerical data for XY type lattice models [4]. Furthermore, Borel resummed results on the basis of four-loop perturbation series [5] are presented for the universal amplitude ratios $P=(1-A^+/A^-)/\alpha$ related to the specific heat and for $R_\xi^T$ related to the superfluid density. While our result for $R_\xi^T$ is in good agreement with experiments [6] our result for $P=4.433 \pm 0.077$ disagrees with both experimental [1] and numerical results [7]. Further theoretical and experimental investigations are required to resolve these discrepancies. 1) J.A. Lipa et al., Phys. Rev. B 68, 174518 (2003) \newline 2) R. Guida, J. Zinn-Justin, J. Phys. A 31, 8103 (1998) \newline 3) D.B. Murray, B.G. Nickel (unpublished) \newline 4) M. Campostrini et al., Phys. Rev. B 74, 14450 (2006) \newline 5) M. Stroesser, V. Dohm, Phys. Rev. E 67, 056115 (2003) \newline 6) A. Singsaas, G. Ahlers, Phys. Rev. B 30, 5103 (1984) \newline 7) M. Hasenbusch, J. Stat Mech. P08019 (2006)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Cremer, D. and Dohm, V.}, biburl = {https://www.bibsonomy.org/bibtex/25c8b113b8218a4e4fba219db80662b4e/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {fdef648643d727f982cb37f3e43017ea}, intrahash = {5c8b113b8218a4e4fba219db80662b4e}, keywords = {amplitude borel critical exponents helium lambda ratios statphys23 summation topic-2 transition universal}, month = {9-13 July}, timestamp = {2007-06-20T10:16:31.000+0200}, title = {Precision results from improved Borel summation of critical exponents and amplitude ratios of the $d=3, n=2$ universality class}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=850}, year = 2007 }