1,935 research outputs found
Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation
The critical behavior of the two-dimensional N-vector cubic model is studied
within the field-theoretical renormalization-group (RG) approach. The
beta-functions and critical exponents are calculated in the five-loop
approximation, RG series obtained are resummed using Pade-Borel-Leroy and
conformal mapping techniques. It is found that for N = 2 the continuous line of
fixed points is well reproduced by the resummed RG series and an account for
the five-loop terms makes the lines of zeros of both beta-functions closer to
each another. For N > 2 the five-loop contributions are shown to shift the
cubic fixed point, given by the four-loop approximation, towards the Ising
fixed point. This confirms the idea that the existence of the cubic fixed point
in two dimensions under N > 2 is an artifact of the perturbative analysis. In
the case N = 0 the results obtained are compatible with the conclusion that the
impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
- …