1,933 research outputs found
Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations
We resolve the local semistable reduction problem for overconvergent
F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and
residue transcendence degree 0). We first introduce a higher-dimensional
analogue of the generic radius of convergence for a p-adic differential module,
which obeys a convexity property. We then combine this convexity property with
a form of the p-adic local monodromy theorem for so-called fake annuli.Comment: 36 pages; v3: refereed version; adds appendix with two example
What are the Confining Field Configurations of Strong-Coupling Lattice Gauge Theory?
Starting from the strong-coupling SU(2) Wilson action in D=3 dimensions, we
derive an effective, semi-local action on a lattice of spacing L times the
spacing of the original lattice. It is shown that beyond the adjoint
color-screening distance, i.e. for , thin center vortices are stable
saddlepoints of the corresponding effective action. Since the entropy of these
stable objects exceeds their energy, center vortices percolate throughout the
lattice, and confine color charge in half-integer representations of the SU(2)
gauge group. This result contradicts the folklore that confinement in
strong-coupling lattice gauge theory, for D>2 dimensions, is simply due to
plaquette disorder, as is the case in D=2 dimensions. It also demonstrates
explicitly how the emergence and stability of center vortices is related to the
existence of color screening by gluon fields.Comment: 17 pages, 5 figures, latex2
Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
We reconsider the conceptual foundations of the renormalization-group (RG)
formalism, and prove some rigorous theorems on the regularity properties and
possible pathologies of the RG map. Regarding regularity, we show that the RG
map, defined on a suitable space of interactions (= formal Hamiltonians), is
always single-valued and Lipschitz continuous on its domain of definition. This
rules out a recently proposed scenario for the RG description of first-order
phase transitions. On the pathological side, we make rigorous some arguments of
Griffiths, Pearce and Israel, and prove in several cases that the renormalized
measure is not a Gibbs measure for any reasonable interaction. This means that
the RG map is ill-defined, and that the conventional RG description of
first-order phase transitions is not universally valid. For decimation or
Kadanoff transformations applied to the Ising model in dimension ,
these pathologies occur in a full neighborhood of the low-temperature part of the first-order
phase-transition surface. For block-averaging transformations applied to the
Ising model in dimension , the pathologies occur at low temperatures
for arbitrary magnetic-field strength. Pathologies may also occur in the
critical region for Ising models in dimension . We discuss in detail
the distinction between Gibbsian and non-Gibbsian measures, and give a rather
complete catalogue of the known examples. Finally, we discuss the heuristic and
numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also
ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.
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