1,817 research outputs found
Temperature Dependence of Facet Ridges in Crystal Surfaces
The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model
on a honeycomb lattice is studied numerically. We focus on the facet ridge
endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth
in the exactly soluble square lattice BCSOS model. In our more general context
the transfer matrix is not stochastic at the FRE points, and a more complex
structure develops. We observe ridge lines sticking into the rough phase where
thesurface orientation jumps inside the rounded part of the crystal. Moreover,
the rough-to-faceted edges become first-order with a jump in surface
orientation, between the FRE point and Pokrovsky-Talapov (PT) type critical
endpoints. The latter display anisotropic scaling with exponent instead
of familiar PT value .Comment: 12 pages, 19 figure
Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
We use the structure lattice, introduced in Part I, to undertake a systematic
study of the class consisting of compactly generated,
topologically simple, totally disconnected locally compact groups that are
non-discrete. Given , we show that compact open subgroups of
involve finitely many isomorphism types of composition factors, and do not
have any soluble normal subgroup other than the trivial one. By results of Part
I, this implies that the centraliser lattice and local decomposition lattice of
are Boolean algebras. We show that the -action on the Stone space of
those Boolean algebras is minimal, strongly proximal, and micro-supported.
Building upon those results, we obtain partial answers to the following key
problems: Are all groups in abstractly simple? Can a group in
be amenable? Can a group in be such that the
contraction groups of all of its elements are trivial?Comment: 82 page
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