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We improve the theoretical estimates of the critical exponents for thethree-dimensional XY universality class, which apply to the superfluidtransition in He4 along the lambda-line of its phase diagram. We obtain theestimates alpha=-0.0151(3), nu=0.6717(1), eta=0.0381(2), gamma=1.3178(2),beta=0.3486(1), and delta=4.780(1). Our results are obtained by finite-sizescaling analyses of high-statistics Monte Carlo simulations up to lattice sizeL=128 and resummations of 22nd-order high-temperature expansions of twoimproved models with suppressed leading scaling corrections. We note that ourresult for the specific-heat exponent alpha disagrees with the most recentexperimental estimate alpha=-0.0127(3) at the superfluid transition of He4 inmicrogravity environment.Comment: 45 pages, 16 fig

physical review. b, condensed matter and materials physics

Theoretical estimates of the critical exponents of the superfluid transition in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi>He</mml:mi><mml:none /><mml:none /><mml:mprescripts /><mml:none /><mml:mn>4</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>by lattice methods

Theoretical estimates of the critical exponents of the superfluid transition inHe4by lattice methods