18,151 research outputs found
On free energies of the Ising model on the Cayley tree
We present, for the Ising model on the Cayley tree, some explicit formulae of
the free energies (and entropies) according to boundary conditions (b.c.). They
include translation-invariant, periodic, Dobrushin-like b.c., as well as those
corresponding to (recently discovered) weakly periodic Gibbs states. The later
are defined through a partition of the tree that induces a 4-edge-coloring. We
compute the density of each color.Comment: 18 pages, 4 figure
Feynman-Hellmann theorem for resonances and the quest for QCD exotica
The generalization of the Feynman-Hellmann theorem for resonance states in
quantum field theory is derived. On the basis of this theorem, a criterion is
proposed to study the possible exotic nature of certain hadronic states
emerging in QCD. It is shown that this proposal is supported by explicit
calculations in Chiral Perturbation Theory and by large- arguments.
Analyzing recent lattice data on the quark mass dependence in the pseudoscalar,
vector meson, baryon octet and baryon decuplet sectors, we conclude that, as
expected, these are predominately quark-model states, albeit the corrections
are non-negligible.Comment: 26 pages, 2 figure
On -adic Gibbs Measures for Hard Core Model on a Cayley Tree
In this paper we consider a nearest-neighbor -adic hard core (HC) model,
with fugacity , on a homogeneous Cayley tree of order (with neighbors). We focus on -adic Gibbs measures for the HC model, in
particular on -adic "splitting" Gibbs measures generating a -adic Markov
chain along each path on the tree. We show that the -adic HC model is
completely different from real HC model: For a fixed we prove that the
-adic HC model may have a splitting Gibbs measure only if divides
. Moreover if divides but does not divide then there
exists unique translational invariant -adic Gibbs measure. We also study
-adic periodic splitting Gibbs measures and show that the above model admits
only translational invariant and periodic with period two (chess-board) Gibbs
measures. For (resp. ) we give necessary and sufficient
(resp. necessary) conditions for the existence of a periodic -adic measure.
For k=2 a -adic splitting Gibbs measures exists if and only if p=3, in this
case we show that if belongs to a -adic ball of radius 1/27 then
there are precisely two periodic (non translational invariant) -adic Gibbs
measures. We prove that a -adic Gibbs measure is bounded if and only if
.Comment: 17 page
On the Four-Dimensional Diluted Ising Model
In this letter we show strong numerical evidence that the four dimensional
Diluted Ising Model for a large dilution is not described by the Mean Field
exponents. These results suggest the existence of a new fixed point with
non-gaussian exponents.Comment: 9 pages. compressed ps-file (uufiles
A new scaling property of turbulent flows
We discuss a possible theoretical interpretation of the self scaling property
of turbulent flows (Extended Self Similarity). Our interpretation predicts
that, even in cases when ESS is not observed, a generalized self scaling, must
be observed. This prediction is checked on a number of laboratory experiments
and direct numerical simulations.Comment: Plain Latex, 1 figure available upon request to
[email protected]
Atomic excitations during the nuclear {\ss}- decay in light atoms
Probabilities of various final states are determined numerically for a number
of {\ss}- decaying light atoms. In our evaluations of the final state
probabilities we have used the highly accurate atomic wave functions
constructed for each few-electron atom/ion. We also discuss an experimental
possibility to observe negatively charged ions which form during the nuclear
{\ss}+ decays. High order corrections to the results obtained for {\ss}+/-
decays in few-electron atoms with the use of sudden approximation are
considered.Comment: 26 pages, 40 references, 6 tables and 0 figure
- …