My current interests are the following:

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.