1,765 research outputs found
Recursion Relations in -adic Mellin Space
In this work, we formulate a set of rules for writing down -adic Mellin
amplitudes at tree-level. The rules lead to closed-form expressions for Mellin
amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in
nature, with two different physical interpretations: one as a recursion on the
number of internal lines in the diagram, and the other as reminiscent of
on-shell BCFW recursion for flat-space amplitudes, especially when viewed in
auxiliary momentum space. The prescriptions are proven in full generality, and
their close connection with Feynman rules for real Mellin amplitudes is
explained. We also show that the integrands in the Mellin-Barnes representation
of both real and -adic Mellin amplitudes, the so-called pre-amplitudes, can
be constructed according to virtually identical rules, and that these
pre-amplitudes themselves may be re-expressed as products of particular Mellin
amplitudes with complexified conformal dimensions.Comment: 45 pages + appendices, several figure
On dynamical systems and phase transitions for -state -adic Potts model on the Cayley tree
In the present paper, we introduce a new kind of -adic measures for
-state Potts model, called {\it -adic quasi Gibbs measure}. For such a
model, we derive a recursive relations with respect to boundary conditions.
Note that we consider two mode of interactions: ferromagnetic and
antiferromagnetic. In both cases, we investigate a phase transition phenomena
from the associated dynamical system point of view. Namely, using the derived
recursive relations we define one dimensional fractional -adic dynamical
system. In ferromagnetic case, we establish that if is divisible by ,
then such a dynamical system has two repelling and one attractive fixed points.
We find basin of attraction of the fixed point. This allows us to describe all
solutions of the nonlinear recursive equations. Moreover, in that case there
exists the strong phase transition. If is not divisible by , then the
fixed points are neutral, and this yields that the existence of the quasi phase
transition. In antiferromagnetic case, there are two attractive fixed points,
and we find basins of attraction of both fixed points, and describe solutions
of the nonlinear recursive equation. In this case, we prove the existence of a
quasi phase transition.Comment: 29 pages, 1 figur
The Lawson-Yau formula and its generalization
AbstractThe Euler characteristic of Chow varieties of algebraic cycles of a given degree in complex projective spaces was computed by Blaine Lawson and Stephen Yau by using holomorphic symmetries of cycles spaces. In this paper we compute this in a direct and elementary way and generalize this formula to the l-adic Euler–Poincaré characteristic for Chow varieties over any algebraically closed field. Moreover, the Euler characteristic for Chow varieties with certain group action is calculated. In particular, we calculate the Euler characteristic of the space of right quaternionic cycles of a given dimension and degree in complex projective spaces
On Phase Transitions for -Adic Potts Model with Competing Interactions on a Cayley Tree
In the paper we considere three state -adic Potts model with competing
interactions on a Cayley tree of order two. We reduce a problem of describing
of the -adic Gibbs measures to the solution of certain recursive equation,
and using it we will prove that a phase transition occurs if and only if
for any value (non zero) of interactions. As well, we completely solve the
uniqueness problem for the considered model in a -adic context. Namely, if
then there is only a unique Gibbs measure the model.Comment: 12 pages, to appear in the Proceedings of the '2nd International
Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 September 2005)
published by AIP Conference Proceeding
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