Dual description of η-deformed OSP sigma models

We study the dual description of the η-deformed OSP(N|2m) sigma model in the asymptotically free regime (N > 2m + 2). Compared to the case of classical Lie groups, for supergroups there are inequivalent η-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter b, which defines the η-deformed OSP(N|2m) sigma model in the limit b → ∞ and a certain Toda QFT as b → 0. In the sigma model regime we show that the leading UV asymptotic of the η-deformed model coincides with a perturbed Gaussian theory. In the perturbative regime b → 0 we show that the tree-level two-particle scattering matrix matches the expansion of the trigonometric OSP(N|2m) S-matrix.

Grassmannization of the 3D Ising Model

The application of Feynman’s diagrammatic technique to classical link models with local constraints seems impossible due to (i) the absence of a free Gaussian theory on top of which the perturbative expansion can be constructed, and (ii) Dyson’s collapse argument, rendering the perturbative expansion divergent. However, we show for the classical 3D Ising model how both problems can be circumvented using a Grassmann representation. This makes it possible to obtain an expansion of the spin correlation function and the magnetic susceptibility in terms of the inverse temperature in the thermodynamic limit, through which the values for the critical temperature and critical index g are evaluated within 1.6% and 5.4% of their accepted values, respectively. Our work is a straightforward adaptation of the theory previously developed in an earlier paper.

An Improved Non-Gaussian Statistical Theory of Rubber Elasticity for Short Chains

The mechanical behavior of polymers has long been described by the non-Gaussian statistical model. Non-Gaussian models are generally based on the Kuhn-Grün (KG) distribution function, which itself is derived from the first order approximation of the complex Rayleigh’s exact Fourier integral distribution. The KG function has gained such a broad acceptance in the field of polymer physics that the non-Gaussian theory is often used to describe chains with various flexibility ratios. However, KG function is shown to be only relevant for long chains, with more than 40 segments. Here, we propose a new accurate approximation of the entropic force resulted from Rayleigh distribution function of non-Gaussian chains. The approximation provides an improved version of inverse Langevin function which has a limited error value with respect to the exact entropic force. The proposed function provides a significantly more accurate estimation of the distribution function than KG functions for small and medium-sized chains with less than 40 segments.

Correlation Functions, Universal Ratios and Goldstone Mode Singularities in n-Vector Models

Correlation functions in the (n) models below the critical temperature are considered. Based on Monte Carlo (MC) data, we confirm the fact stated earlier by Engels and Vogt, that the transverse two-plane correlation function of the (4) model for lattice sizes about L = 120 and small external fields h is very well described by a Gaussian approximation. However, we show that fits of not lower quality are provided by certain non-Gaussian approximation. We have also tested larger lattice sizes, up to L = 512. The Fourier-transformed transverse and longitudinal two-point correlation functions have Goldstone mode singularities in the thermodynamic limit at k → 0 and h = +0, i.e., G⊥ (k) ≃ ak–λ⊥ and G‖(k)≃bk–λ‖, respectively. Here a and b are the amplitudes, k = |k| is the magnitude of the wave vector k. The exponents λᚆ, λ‖ and the ratio bM2/a2, where M is the spontaneous magnetization, are universal according to the GFD (grouping of Feynman diagrams) approach. Here we find that the universality follows also from the standard (Gaussian) theory, yielding bM2/a2=(n−1)/16. Our MC estimates of this ratio are 0.06±0.01 for n=2, 0.17±0.01 for n = 4 and 0.498±0.010 for n = 10. According to these and our earlier MC results, the asymptotic behavior and Goldstone mode singularities are not exactly described by the standard theory. This is expected from the GFD theory. We have found appropriate analytic approximations for G⊥(k) and G‖(k), well fitting the simulation data for small k. We have used them to test the Patashinski-Pokrovski relation and have found that it holds approximately.

Georg von Neumayer and geomagnetic research

Neumayer was a prominent figure in the development of geophysics in the 19th century from a scientific as well as from an organisational point of view. In this paper we review and highlight his activities and efforts in geomagnetic research within five different aspects of geomagnetism: regional geomagnetic surveys, geomagnetic work in German naval observatories, geomagnetic investigations during the First Polar Year 1882/83, modifications of the Gaussian theory, and geomagnetic charts. In each field Neumayer was a researcher, a thinker, and a stimulating coordinator.