We improve the theoretical estimates of the critical exponents for the three-dimensional $XY$ universality class that apply to the superfluid transition in $^{4}\mathrm{He}$ along the $\ensuremath{\lambda}$ line of its phase diagram. We obtain the estimates $\ensuremath{\alpha}=\ensuremath{-}0.0151(3)$, $\ensuremath{\nu}=0.6717(1)$, $\ensuremath{\eta}=0.0381(2)$, $\ensuremath{\gamma}=1.3178(2)$, $\ensuremath{\beta}=0.3486(1)$, and $\ensuremath{\delta}=4.780(1)$. Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size $L=128$ and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent $\ensuremath{\alpha}$ disagrees with the most recent experimental estimate $\ensuremath{\alpha}=\ensuremath{-}0.0127(3)$ at the superfluid transition of $^{4}\mathrm{He}$ in a microgravity environment.We improve the theoretical estimates of the critical exponents for the three-dimensional $XY$ universality class that apply to the superfluid transition in $^{4}\mathrm{He}$ along the $\ensuremath{\lambda}$ line of its phase diagram. We obtain the estimates $\ensuremath{\alpha}=\ensuremath{-}0.0151(3)$, $\ensuremath{\nu}=0.6717(1)$, $\ensuremath{\eta}=0.0381(2)$, $\ensuremath{\gamma}=1.3178(2)$, $\ensuremath{\beta}=0.3486(1)$, and $\ensuremath{\delta}=4.780(1)$. Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size $L=128$ and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent $\ensuremath{\alpha}$ disagrees with the most recent experimental estimate $\ensuremath{\alpha}=\ensuremath{-}0.0127(3)$ at the superfluid transition of $^{4}\mathrm{He}$ in a microgravity environment.

arXiv:cond-mat/0605083Physical Review BOct 6, 2006269 citations

Critical exponents from power spectra

K. B. Lauritsen, Hans C. Fogedby

Journal of Statistical PhysicsJul 1, 199325 citations

Surface Critical Behavior in Fixed Dimensions d<4 : Nonanalyticity of Critical Surface Enhancement and Massive Field Theory Approach

Hans Werner Diehl, Mykola A. Shpot

The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented. Two-loop calculations and subsequent Pad\'e-Borel analyses of surface critical exponents of the special and ordinary phase transitions yield estimates in reasonable agreement with recent Monte Carlo results. This includes the crossover exponent $\ensuremath{\Phi}(d=3)$, for which we obtain the values $\ensuremath{\Phi}(n=1)\ensuremath{\simeq}0.54$ and $\ensuremath{\Phi}(n=0)\ensuremath{\simeq}0.52$, considerably lower than the previous $\ensuremath{\epsilon}$-expansion estimates.The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented. Two-loop calculations and subsequent Pad\'e-Borel analyses of surface critical exponents of the special and ordinary phase transitions yield estimates in reasonable agreement with recent Monte Carlo results. This includes the crossover exponent $\ensuremath{\Phi}(d=3)$, for which we obtain the values $\ensuremath{\Phi}(n=1)\ensuremath{\simeq}0.54$ and $\ensuremath{\Phi}(n=0)\ensuremath{\simeq}0.52$, considerably lower than the previous $\ensuremath{\epsilon}$-expansion estimates.

arXiv:cond-mat/9409064Physical Review LettersDec 19, 199452 citations

Accurate critical exponents from the ε-expansion

J. C. Le Guillou, Jean Zinn‐Justin

Current physics sources and commentsJan 1, 199030 citations

Higher order contributions to critical exponents

E. Brézin, J. C. Le Guillou, Jean Zinn‐Justin +1 more

Physics Letters AJun 1, 1973138 citations

Critical Exponents of the Classical Heisenberg Ferromagnet

Christian Holm, Wolfhard Janke E

In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352, 1996) reported high precision Monte Carlo (MC) estimates of the static critical exponents of the classical 3D Heisenberg model, which stand in sharp contrast to values obtained by four independent approaches, namely by other recent high statistics MC simulations, high-temperature series analyses, field theoretical methods, and experimental studies. In reply to the above cited work we submitted this paper as a comment to Phys. Rev. Lett.In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352, 1996) reported high precision Monte Carlo (MC) estimates of the static critical exponents of the classical 3D Heisenberg model, which stand in sharp contrast to values obtained by four independent approaches, namely by other recent high statistics MC simulations, high-temperature series analyses, field theoretical methods, and experimental studies. In reply to the above cited work we submitted this paper as a comment to Phys. Rev. Lett.

arXiv:hep-lat/9605024Physical Review LettersMar 17, 199718 citations

We improve the theoretical estimates of the critical exponents for the three-dimensional

XY

universality class that apply to the superfluid transition in

^{4}\mathrm{He}

along the $\ensuremath{\lambda}$ line of its phase diagram. We obtain the estimates $\ensuremath{\alpha}=\ensuremath{-}0.0151(3)$, $\ensuremath{\nu}=0.6717(1)$, $\ensuremath{\eta}=0.0381(2)$, $\ensuremath{\gamma}=1.3178(2)$, $\ensuremath{\beta}=0.3486(1)$, and $\ensuremath{\delta}=4.780(1)$. Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size

L=128

and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent $\ensuremath{\alpha}$ disagrees with the most recent experimental estimate $\ensuremath{\alpha}=\ensuremath{-}0.0127(3)$ at the superfluid transition of

^{4}\mathrm{He}

in a microgravity environment.

The critical behavior of semi-infinite systems in fixed dimensions

d<4

is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented. Two-loop calculations and subsequent Pad\'e-Borel analyses of surface critical exponents of the special and ordinary phase transitions yield estimates in reasonable agreement with recent Monte Carlo results. This includes the crossover exponent $\ensuremath{\Phi}(d=3)$, for which we obtain the values $\ensuremath{\Phi}(n=1)\ensuremath{\simeq}0.54$ and $\ensuremath{\Phi}(n=0)\ensuremath{\simeq}0.52$, considerably lower than the previous $\ensuremath{\epsilon}$-expansion estimates.