493 research outputs found

    Mass Expansions of Screened Perturbation Theory

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    The thermodynamics of massless phi^4-theory is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the Lagrangian. We analytically calculate the pressure and entropy to three-loop order and the screening mass to two-loop order, expanding in powers of m/T. The truncated m/T-expansion results are compared with numerical SPT results for the pressure, entropy and screening mass which are accurate to all orders in m/T. It is shown that the m/T-expansion converges quickly and provides an accurate description of the thermodynamic functions for large values of the coupling constant.Comment: 22 pages, 10 figure

    Pressure to order g8log(g)g^8*log(g) in ϕ4\phi^4-theory at weak coupling

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    We calculate the pressure of massless ϕ4\phi^4-theory to order g8log(g)g^8\log(g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order TT and the soft momentum scale of order gTgT. Effective field theory methods and dimensional reduction are used to separate the contributions from the two momentum scales: The hard contribution can be calculated as a power series in g2g^2 using naive perturbation theory with bare propagators. The soft contribution can be calculated using an effective theory in three dimensions, whose coefficients are power series in g2g^2. This contribution is a power series in gg starting at order g3g^3. The calculation of the hard part to order g6g^6 involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schr\"oder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order g6g^6 and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order g7g^7. The coefficients of the effective theory satisfy a set of renormalization group equations that can be used to sum up leading and subleading logarithms of T/gTT/gT. We use the solutions to these equations to obtain a result for the free energy which is correct to order g8log(g)g^8\log(g). Finally, we investigate the convergence of the perturbative series.Comment: 29 pages and 12 figs. New version: we have pushed the calculations to g^8*log(g) using the renormalization group to sum up log(g) from higher orders. Published in JHE

    Screened Perturbation Theory to Three Loops

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    The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast to the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.Comment: 30 pages, 10 figure

    Three-loop HTL gluon thermodynamics at intermediate coupling

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    We calculate the thermodynamic functions of pure-glue QCD to three-loop order using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature quantum field theory. We show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T3  TcT\simeq3\;T_c. Our results suggest that HTLpt provides a systematic framework that can used to calculate static and dynamic quantities for temperatures relevant at LHC.Comment: 24 pages, 13 figs. 2nd version: improved discussion and fixing typos. Published in JHE

    Thermal Effects in Low-Temperature QED

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    QED is studied at low temperature (TmT\ll m, where mm is the electron mass) and zero chemical potential. By integrating out the electron field and the nonzero bosonic Matsubara modes, we construct an effective three-dimensional field theory that is valid at distances R1/TR\gg1/T. As applications, we reproduce the ring-improved free energy and calculate the Debye mass to order e5e^5.Comment: 20 pages, 4 figures, revte

    Polymeric strontium ranelate nonahydrate

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    The title compound, poly[[μ-aqua-tetraaqua{μ-5-[bis(carboxylatomethyl)amino]-3-carboxylatomethyl-4-cyanothiophene-2-carboxylato}distrontium(II)] tetrahydrate], [Sr2(C12H6N2O8S)(H2O)5]·3.79H2O, crystallizes with nine- and eight-coordinated Sr2+ cations. They are bound to seven of the eight ranelate O atoms and five of the water molecules. The SrO8 and SrO9 polyhedra are interconnected by edge-sharing, forming hollow layers parallel to (011). The layers are, in turn, interconnected by ranelate anions, forming a metal–organic framework (MOF) structure with channels along the a axis. The four water molecules not coordinated to strontium are located in these channels and hydrogen bonded to each other and to the ranelates. Part of the water H atoms are disordered. The compound dehydrates very easily and 0.210 (4) water molecules out of nine were lost during crystal mounting causing additional disorder in the water structure
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