Critical exponents for a $d$-dimensional system with an isotropic $n$-component order parameter and long-range attractive interactions decaying as $\frac{1}{{r}^{d+\ensuremath{\sigma}}} (\ensuremath{\sigma}>0)$ are derived, using the renormalization group approach, power series in $\ensuremath{\epsilon}=2\ensuremath{\sigma}\ensuremath{-}d>0$ ($\ensuremath{\sigma}\ensuremath{\ne}2$, fixed) or $\ensuremath{\Delta}\ensuremath{\sigma}=\ensuremath{\sigma}\ensuremath{-}\frac{1}{2}d>0$ ($d$ and,...

Recent results giving both the asymptotic behavior and explicit values of leading-order perturbation-expansion terms in fixed dimension for coefficients Callan-Symanzik equation are analyzed by Borel-Leroy, Pad\'e-approximant method $n$-component ${\ensuremath{\varphi}}^{4}$ model. Estimates critical exponents these models obtained $n=0, 1, 2, \mathrm{and} 3$ three dimensions with a typical accuracy few one thousandths. In two less accurate obtained.

The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an $\mathrm{exp}(\ensuremath{-}A{s}^{4}+B{s}^{2})$ spin-weight factor are expanded dimensionless, renormalized coupling constant. These series summed by Pad\'e-Borel method to yield critical indices $\ensuremath{\gamma}=1.241\ifmmode\pm\else\textpm\fi{}0.002$, $\ensuremath{\eta}=0.02\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\nu}=0.63\ifmmode\pm\else\textpm\fi{}0.01$, and...

We present the first detailed calculations in ordered phase using massive ${\ensuremath{\varphi}}^{4}$ field theory directly at d=3. It is shown that an adapted expansion allows renormalization functions of symmetric to be kept unchanged. Extending results a previous paper [C. Bagnuls and C. Bervillier, Phys. Rev. B 32, 7209 (1985)] (noted I), we obtain, for Ising-type systems, nonasymptotic temperature spontaneous magnetization, susceptibility, specific heat along critical isochore, which...

High-temperature series for two bcc lattice models which interpolate between the Gaussian (or free-field) model and $S=\frac{1}{2}$ Ising are analyzed by partial differential approximants. Series to order 21 in both $x\ensuremath{\propto}\frac{1}{T}$ interpolation parameter, $y$, yield unbiased estimates correction-to-scaling exponent, $\ensuremath{\theta}=0.54\ifmmode\pm\else\textpm\fi{}5$, susceptibility $\ensuremath{\gamma}=1.2385\ifmmode\pm\else\textpm\fi{}15$. The results universal...

We present results of model calculations based on two different approximations which were both intended to be improvements over the coherent potential approximation. show that yield nonphysical solutions; specifically, they predict average Green's functions contain singularities upper and lower halves complex energy plane. conjecture nonanalytic behavior will occur generally in high-order function.

We describe a simple generalization of the coherent-potential approximation that is exactly equivalent to self-contained cumulant expansions and self-consistent diagrammatic-resummation techniques. A detailed analysis these different methods for pair case given.

We present a simple derivation of the mean square end-to-end distance 〈R2〉 linear flexible chain as perturbation series in dimensionless excluded volume parameter zd. Our results, to orders six and four space dimension d=3 2, respectively, are 〈R2〉= Ll[1+ (4)/(3) z3−2.075 385 396 z23+6.296 879 676 z33 GFIX−25.057 250 72 z43+116.134 785 z53 GFIX−594.716 63 z63+⋅⋅⋅], d=3, 1/2 z2−0.121 545 25 z22+0.026 631 36 z32 GFIX−0.132 236 03 z42+⋅⋅⋅], d=2, where z3=(3/2πl)3/2 wL1/2 z2=wL/πl with L contour...

We present explicit values of the mean square end-to-end distance 〈R2〉 a linear flexible chain for all excluded volume parameter z>0 in space dimension 3. Our results are obtained by performing series analyses our earlier sixth-order perturbation calculation using Borel summation technique and consideration second virial coefficient. The philosophy is essentially same as that Le Guillou Zinn-Justin [Phys. Rev. B 21, 3976 (1980)]. Changes with theory order technical variations analysis...

The coherent potential approximation (CPA) has been generalized to describe spin waves in a dilute Heisenberg ferromagnet at T=0. full T matrix of an isolated vacancy effective medium is evaluated and the self-energy obtained selfconsistently. In order project out spurious degrees freedom associated with fictitious spins on sites, class pseudopotentials are constructed. response functions G(k, omega ) density states rho ( for two such detail. had core pseudopotential found yield best CPA...

Some simplifications of the integrals (2n+1), derived by Wu et al (1976 13 316), that contribute to zero field susceptibility 2D square lattice Ising model are reported. In particular, several alternate expressions for integrands in (2n+1) determined which greatly facilitate both generation high-temperature series and analytical analysis. One can show as series, = 22n(s/2)4n(n+1)(1+O(s)) where s is variable sin(2K) with K conventional normalized inverse temperature. Analysis near symmetry...

We present a modified probability distribution for single stiff chain. This includes the usual Wiener measure that accounts bond length and term associates an explicit energy with bending of The modification additional factors suppress end fluctuations to make chain homogeneous. Our result mean squared end-to-end distance is Kratky–Porod but analysis clarifies number points in literature.

Using optical microscopy, we have measured the formation and growth of holes in freely standing polystyrene films melt state. For all films, observed exponential hole radius uniform thickening. Our measurements are interpreted terms dependence viscosity on shear strain rate associated with process. The measurement thin polymer provides a unique probe nonlinear viscoelastic effects confined polymers.

We propose a relation which predicts the low-frequency thermal conductivity of one-dimensional (1D) system from and bulk viscosity at higher frequency. Our theory is based on assumption that ``ballistic'' transport by sound waves dominates heat transport. For with equal capacities $({c}_{p}={c}_{v})$ this particularly simple. test prediction simulating chain particles quartic interparticle potentials under zero pressure conditions. As frequency $\ensuremath{\omega}\ensuremath{\rightarrow}0$...

The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps simplest system in which one can study generation small scales by stretching resulting turbulence. problem studied direct spectral numerical solution Navier–Stokes equations (with up to 2563 modes) power-series analysis time.The strongly influenced symmetries confine an impermeable box with stress-free boundaries. There early stage during anisotropic...

We study the diffusion-controlled process of cluster growth, introduced by Witten and Sander, on a Cayley tree. show that it is then equivalent to Eden model where growth occurs at any boundary site with equal probability. The mean level number square gyration radius an $N$-particle aggregate both increase as $[\frac{K}{(K\ensuremath{-}1)}]\mathrm{ln}N$ tree branching ratio $K$. case biased diffusion studied numerically: attractive bias does not change logarithmic behavior size, but...

A modified form of percolation theory is solved exactly on a Cayley tree arbitrary coordination number. In this model, cluster growth proceeds "dynamically" by invasion along path least resistance. Although there are clear parallels to ordinary "static" at the threshold, also significant differences. particular, scaling function which describes shape large clusters different in two models.

A remarkable product formula first derived by Palmer and Tracy (1981 Adv. Appl. Math.2329) for the integrand of two-dimensional Ising model susceptibility expansion coefficients (2n )for temperatures Tless than critical Tcis shown to apply equally +1)for T >Tcand agrees with formulae Yamada (1984 Prog. Theor. Phys.711416). This new representation simplifies derivation results in original paper this title (1999 J. Phys. A: Math. Gen.323889) extent that leading series behaviour singularity...