Theory and Satellite Experiment for Critical Exponent alpha of lambda-Transition in Superfluid Helium

On the basis recent seven-loop perturbation expansion for nu^{-1} = 3/(2 - alpha) we perform a careful reinvestigation of the critical exponent alpha governing the power behavior |T_c-T|^{- alpha} of the specific heat of superfluid helium near the phase transition. With the help of variational strong-coupling theory. we find alpha = - 0.01126 +- 0.0010, in very good agreement with the space shuttle experimental value alpha = - 0.01056 +- 0.00038.Comment: Final version to be printed in Phys. Lett. A. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/28

Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory

For an anisotropic euclidean $\phi^4$-theory with two interactions [u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for $M \geq 3$ is found, implying that the critical exponents in the magnetic phase transition of real crystals are of the cubic universality class. There were previous indications of the stability based either on lower-loop expansions or on less reliable Pad\'{e approximations, but only the evidence presented in this work seems to be sufficently convincing to draw this conclusion.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.htm

Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length

We extend previous work on applying the epsilon-expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in epsilon=4-d, where d is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure

Developments in the South Staffordshire iron and steel industry, 1850-1913, in the light of home and foreign competition

When Ebenezer Parkes was discussing the question of foreign competition as it affected the local iron and steel industry at the turn of the century, he stressed that it was a 'many sided thing'. Besides, if South Staffordshire was to reassert itself, then improvements would have to come about in a number of areas - in education, use of labour-saving machinery, practices in the blast furnace and rolling-mill departments, labour relations, canal and rail transport, structure of industry, state support and Colonial trade. This thesis is an attempt to look at the various 'sides' of the South Staffordshire iron and steel industry as it faced up to increasing competition both from other United Kingdom districts and from abroad. The importance of physical factors is considered in conjunction with human ones. Clearly, South Staffordshire could do nothing to prevent the growth of new centres of iron and steel production; furthermore, other older centres of production, notably South Wales and Scotland, fared better in the second half of the nineteenth century because of their tidal locations. Iron ores from Spain or steel 'semis' from the United States or the European Continent tended to emphasise the shift away from a land-locked centre of production. Abroad, tremendous growth was experienced by the iron and steel industries of the United States and Germany, a development which made all the apparent disadvantages of South Staffordshire appear that much more significant. Of these disadvantages, South Staffordshire's almost total dependence on outside supplies of metallurgical coke ranks very high. So, too, do the numerous shortcomings of the transport facilities of the area. On the human side, the failure of the local ironmasters to take full advantage of the proximity of East Midland iron ore supplies was crucial. Their reliance upon outside supplies of iron are, which remained largely out of their control, put them in sharp contrast with producers on the Continent or in the United states. To add to the difficulties being experienced by the local industry, Birmingham and the Black Country proved a very attractive market for foreign producers. The so-called 'dumping' policies of the Americans and Continentals are pursued at some length in the last chapter. Despite the many changes which took place in the district, South Staffordshire remained a very important part of the United Kingdom iron and steel industry. The fortunes of Round Oak, and especially those of Sir Alfred Hickman's Spring Vale Works, illustrate the fact that overall the situation in South Staffordshire was never a totally hopeless one

High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model

We report measurements of the critical exponents of the classical three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with $L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long single-cluster Monte Carlo simulations near the phase transition. We compute high precision estimates of the critical coupling $K_c$, Binder's parameter $U^* and the critical exponents$\nu,\beta / \nu, \eta$, and$\alpha / \nu$, using extensively histogram reweighting and optimization techniques that allow us to keep control over the statistical errors. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition as compared to local update algorithms. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first version arrived incomplete due to mailer problems

Obtaining Bounds on The Sum of Divergent Series in Physics

Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by applying it to various examples, physical and mathematical.Comment: 33 pages, Journal Versio

Finite size effects on measures of critical exponents in d=3 O(N) models

We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with $\epsilon$-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the $\nu$ exponents and critical couplings.Comment: 12 pages, 2 postscript figure