410,118 research outputs found
Metastable states of a ferromagnet on random thin graphs
We calculate the mean number of metastable states of an Ising ferromagnet on
random thin graphs of fixed connectivity c. We find, as for mean field spin
glasses that this mean increases exponentially with the number of sites, and is
the same as that calculated for the +/- J spin glass on the same graphs. An
annealed calculation of the number of metastable states of energy E
is carried out. For small c, an analytic result is obtained. The result is
compared with the one obtained for spin glasses in order to discuss the role
played by loops on thin graphs and hence the effect of real frustration on the
distribution of metastable states.Comment: 15 pages, 3 figure
On graph equivalences preserved under extensions
Let R be an equivalence relation on graphs. By the strengthening of R we mean
the relation R' such that graphs G and H are in the relation R' if for every
graph F, the union of the graphs G and F is in the relation R with the union of
the graphs H and F. We study strengthenings of equivalence relations on graphs.
The most important case that we consider concerns equivalence relations defined
by graph properties. We obtain results on the strengthening of equivalence
relations determined by the properties such as being a k-connected graph,
k-colorable, hamiltonian and planar
Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinity
We study constant mean curvature 1/2 surfaces in H2xR that admit a
compactification of the mean curvature operator. We show that a particular
family of complete entire graphs over H2 admits a structure of infinite
dimensional manifold with local control on the behaviors at infinity. These
graphs also appear to have a half-space property and we deduce a uniqueness
result at infinity. Deforming non degenerate constant mean curvature 1/2
annuli, we provide a large class of (non rotational) examples and construct
(possibly embedded) annuli without axis, i.e. with two vertical, asymptotically
rotational, non aligned ends.Comment: 35 pages. Addition of a half-space theore
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