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

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

Application of Minimal Subtraction Renormalization to Crossover Behavior near the 3^3He Liquid-Vapor Critical Point

Parametric expressions are used to calculate the isothermal susceptibility, specific heat, order parameter, and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region. These expressions are based on the minimal-subtraction renormalization scheme within the $\phi^4$ model. Using two adjustable parameters in these expressions, we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and early measurements of coexistence curve and light scattering intensity along the critical isochore of $^3$He near its liquid-vapor critical point. The theory provides good agreement with these experimental measurements within the reduced temperature range $|t| \le 2\times 10^{-2}$

Synthesis of intermetallic hydrogen storage materials based on TI-CR by glow discharge plasma

The TiCr2 intermetallic compound with the C36 hexagonal Laves phase has been synthesized by glow discharge plasma. The hydrogen absorption-desorption properties of the obtained alloy were investigated. It is shown that hydrogen storage capacity of material was 0.43 wt % at 85 °C and 8 atm

Effective critical behaviour of diluted Heisenberg-like magnets

In agreement with the Harris criterion, asymptotic critical exponents of three-dimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration- and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field--theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point $T_c$ as observed experimentally. In the asymptotic limit (at $T_c$) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.Comment: 15 pages, 4 figure

Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions

We present an analytic five-loop calculation for the additive renormalization constant A(u,epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric phi^4 theory within the minimal subtraction scheme. We show that this calculation does not require new five-loop integrations but can be performed on the basis of the previous five-loop calculation of the four-point vertex function combined with an appropriate identification of symmetry factors of vacuum diagrams. We also determine the amplitude functions of the specific heat in three dimensions for n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude functions for n=1. Previous conjectures regarding the smallness of the resummed higher-order contributions are confirmed. Borel resummed universal amplitude ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.

Crossover from Isotropic to Directed Percolation

Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic scaling behavior (``self--affinity''). Taking advantage of the fact that both isotropic and directed bond percolation (with one preferred direction) may be mapped onto corresponding variants of (Reggeon) field theory, we discuss the crossover between self--similar and self--affine scaling. This has been a long--standing and yet unsolved problem because it is accompanied by different upper critical dimensions: $d_c^{\rm I} = 6$ for isotropic, and $d_c^{\rm D} = 5$ for directed percolation, respectively. Using a generalized subtraction scheme we show that this crossover may nevertheless be treated consistently within the framework of renormalization group theory. We identify the corresponding crossover exponent, and calculate effective exponents for different length scales and the pair correlation function to one--loop order. Thus we are able to predict at which characteristic anisotropy scale the crossover should occur. The results are subject to direct tests by both computer simulations and experiment. We emphasize the broad range of applicability of the proposed method.Comment: 19 pages, written in RevTeX, 12 figures available upon request (from [email protected] or [email protected]), EF/UCT--94/2, to be published in Phys. Rev. E (May 1994

Model C critical dynamics of random anisotropy magnets

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets the structural disorder is present in a form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching an asymptotic regime.Comment: 8 figures, style files include

The finite-temperature chiral transition in QCD with adjoint fermions

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.Comment: 36 page

Classical-to-critical crossovers from field theory

We extent the previous determinations of nonasymptotic critical behavior of Phys. Rev B32, 7209 (1985) and B35, 3585 (1987) to accurate expressions of the complete classical-to-critical crossover (in the 3-d field theory) in terms of the temperature-like scaling field (i.e., along the critical isochore) for : 1) the correlation length, the susceptibility and the specific heat in the homogeneous phase for the n-vector model (n=1 to 3) and 2) for the spontaneous magnetization (coexistence curve), the susceptibility and the specific heat in the inhomogeneous phase for the Ising model (n=1). The present calculations include the seventh loop order of Murray and Nickel (1991) and closely account for the up-to-date estimates of universal asymptotic critical quantities (exponents and amplitude combinations) provided by Guida and Zinn-Justin [J. Phys. A31, 8103 (1998)].Comment: 4 figs, 4 program documents in appendix, some corrections adde

Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point

We report the details and revised analysis of an experiment to measure the specific heat of helium with subnanokelvin temperature resolution near the lambda point. The measurements were made at the vapor pressure spanning the region from 22 mK below the superfluid transition to 4 uK above. The experiment was performed in earth orbit to reduce the rounding of the transition caused by gravitationally induced pressure gradients on earth. Specific heat measurements were made deep in the asymptotic region to within 2 nK of the transition. No evidence of rounding was found to this resolution. The optimum value of the critical exponent describing the specific heat singularity was found to be a = -0.0127+ - 0.0003. This is bracketed by two recent estimates based on renormalization group techniques, but is slightly outside the range of the error of the most recent result. The ratio of the coefficients of the leading order singularity on the two sides of the transition is A+/A- =1.053+ - 0.002, which agrees well with a recent estimate. By combining the specific heat and superfluid density exponents a test of the Josephson scaling relation can be made. Excellent agreement is found based on high precision measurements of the superfluid density made elsewhere. These results represent the most precise tests of theoretical predictions for critical phenomena to date.Comment: 27 Pages, 20 Figure