Nonlinear models in theoretical investigations

A realistic string model for color-electric flux tube with negative stiffness is proposed to overcome serious consistency problems arising in the previous Polyakov-Kleinert rigid string with a positive curvature term.

In the framework of this model, perturbation computations of an interquark potential are performed. It has been shown that the potential has a Luscher shape at great distances between quarks. In 1/d-component limits, were found the temperature dependence on the effective string tension and an approximate deconfinement temperature for small to moderate temperatures. The results are in good agreement with those obtained by Monte Carlo simulations of lattice gauge models.

At high temperature, the model generates a correct temperature behavior of the squared string tension which is in very good agreement with QCD results, thus producing an important evidence for the negative stiffness of the hadronic strings. All these results show that the proposed string model, in contrast to the standard rigid string, creates a satisfactory description of quark forces in QCD [21].

A geometrical approach for the gauge field models has been elaborated [22]. Investigations of geometrical quantization on manifolds has been performed [23]. Investigations of self-organized criticality are performed. Critical exponents for 2D Abelian sandpile models are computed [24].