My current interests are
1. Investigation of
phase transitions problems of certain models of statistical
mechanics on Bethe lattices. Moreover, the description of the set of
Gibbs measures associated with considered models.
2. Study of statistical
mechanics models on networks and the organization of a randomly
damaged uncorrelated networks with an arbitrary degree distribution
by means of p-adic probability theory approaches. This approach is
based on the investigation of p-adic dynamical systems.
3. Investigations of
ergodic and mixing properties of C*-dynamical systems.
1. Ganikhodjaev N.N.,
Mukhamedov F.M., Mendes J.F.F. On the three state Potts model with
competing interactions on the Bethe lattice, Jour. Stat. Mech. 2006,
P08012, 29 p.
2. Khamraev M.,
Mukhamedov, F. On a class of rational p-adic dynamical systems, Jour.
Math. Anal. Appl. 315(2006), 76--89.
3. Mukhamedov, F.
Rozikov, U. On inhomogeneous p-adic Potts model on a Cayley tree.
Infin. Dimens. Anal. Quantum Probab.
Relat. Top. 8(2005),
No. 2, 277--290.
4. Mukhamedov, F.,
Rozikov, U. On Gibbs measures of models with competing ternary and
binary interactions and corresponding von Neumann algebras. I,II.
Jour. Stat. Phys. 118(2004), 825-848; 119(2005), 427--446.
5. Khamraev M.,
Mukhamedov F.M. On p-adic lambda-model on the Cayley tree, Jour.
Math. Phys. 45(2004), No. 11, 4025--4034.