41 research outputs found
Theory of Impurity Effects on the Spin Nematic State
The effect of magnetic bond disorder in otherwise antiferro nematic ordered
system is investigated. We introduced triangular-shaped ferromagnetic bond
disorder in the S=1 bilinear-biquadratic model on a triangular lattice. It is
shown that the coupling between the impurity magnetic moment and nonmagnetic
excitation in the bulk yields single-moment anisotropy and long-range
anisotropic interaction between impurity magnetic moments. This interaction can
induce unconventional spin-freezing phenomena observed in triangular magnet,
NiGa2S4.Comment: 19 pages, 14 figure
Introductory Notes to Algebraic Statistics
These are the notes of a short course on algebraic
statistics, a new discipline across the fields of statistical modeling
and computational commutativa algebra. The basics of the
theory are provided together with brief reference to applications to
design of experiments, to exponential and graphical models, and
to computational biology
BRST Inner Product Spaces and the Gribov Obstruction
A global extension of the Batalin-Marnelius proposal for a BRST inner product
to gauge theories with topologically nontrivial gauge orbits is discussed. It
is shown that their (appropriately adapted) method is applicable to a large
class of mechanical models with a semisimple gauge group in the adjoint and
fundamental representation. This includes cases where the Faddeev-Popov method
fails. Simple models are found also, however, which do not allow for a
well-defined global extension of the Batalin-Marnelius inner product due to a
Gribov obstruction. Reasons for the partial success and failure are worked out
and possible ways to circumvent the problem are briefly discussed.Comment: 49 pages, 1 figure (included
Deriving Deligne-Mumford Stacks with Perfect Obstruction Theories
We give conditions for a n-connective quasicoherent obstruction theory on a
Deligne-Mumford stack to come from the structure of a connective spectral
Deligne-Mumford stack on the underlying topos.Comment: 25 pages; v.4: Assumptions added to correct Lemma; Main result now
gives necessary and sufficient conditions for an obstruction theory to be
induced by a derived structure; Erratum to published version is to appea
The Galois group of a stable homotopy theory
To a "stable homotopy theory" (a presentable, symmetric monoidal stable
-category), we naturally associate a category of finite \'etale algebra
objects and, using Grothendieck's categorical machine, a profinite group that
we call the Galois group. We then calculate the Galois groups in several
examples. For instance, we show that the Galois group of the periodic
-algebra of topological modular forms is trivial and that
the Galois group of -local stable homotopy theory is an extended version
of the Morava stabilizer group. We also describe the Galois group of the stable
module category of a finite group. A fundamental idea throughout is the purely
categorical notion of a "descendable" algebra object and an associated analog
of faithfully flat descent in this context.Comment: 93 pages. To appear in Advances in Mathematic