Delta Expansion on the Lattice and Dilated Scaling Region

A new kind of delta expansion is applied on the lattice to the d=2 non-linear sigma model at N=infinity and N=1 which corresponds to the Ising model. We introduce the parameter delta for the dilation of the scaling region of the model with the replacement of the lattice spacing a to (1-delta)^{1/2}a. Then, we demonstrate that the expansion in delta admits an approximation of the scaling behavior of the model at both limits of N from the information at a large lattice spacing a.Comment: 11 pages, 18 figure

Moment Approach for Determining the Orbital Elements of an Astrometric Binary with Low Signal-to-noise Ratio

A moment approach for orbit determinations of an astrometric binary with low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period such as Cyg-X1 and also at a star wobbled by planets. As an exact solution to the nonlinearly coupled equation system, the orbital elements are written in terms of the second and third moments of projected positions that are measured by astrometry. This may give a possible estimation of the true orbit.Comment: 18 pages, 5 figures, 1 table; accepted by PAS