On the relationship between sigma models and spin chains

We consider the two-dimensional $\rm O(3)$ non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl.Phys. B336 (1990), 457], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient $\theta$ of the topological term is quantized as $\theta=2\pi s$, with $s$ integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-$s$ Heisenberg model. We generalize the analysis to sigma models with other symmetries.Comment: To appear in Int. J. MOd. Phys.

Searching for Weak or Complex Magnetic Fields in Polarized Spectra of Rigel

Seventy-eight high-resolution Stokes V, Q and U spectra of the B8Iae supergiant Rigel were obtained with the ESPaDOnS spectropolarimeter at CFHT and its clone NARVAL at TBL in the context of the Magnetism in Massive Stars (MiMeS) Large Program, in order to scrutinize this core-collapse supernova progenitor for evidence of weak and/or complex magnetic fields. In this paper we describe the reduction and analysis of the data, the constraints obtained on any photospheric magnetic field, and the variability of photospheric and wind lines.Comment: IAUS272 - Active OB Stars: Structure, Evolution, Mass Loss and Critical Limit