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[en] Using algebraic and field theoretical methods, we study the fractional spin symmetries of the φ1,3 deformation of minimal models. The particular example of the D=2 three state tricritical Potts model is examined in detail. Various models based on subalgebras and appropriate discrete automorphism groups of the two dimensional fractional spin algebra are obtained. General features such as superspace and superfield representations, the Uq(sl2) symmetry, the spontaneous exotic supersymmetry breaking, relations with the N=2 Landau Ginzburg models as well as other things are discussed. (author). 24 refs
[en] Using Monte Carlo simulations, magnetic properties of the ferromagnetic nanoparticles of Ising spin-1 are investigated in the framework of the Ising model. The system is considered to have a Rubik’s cube structure composed of nanocubes having an equivalent exchange coupling, while, between adjacent nanocubes, the exchange coupling is assumed to vary. Both size effects and system parameters’ influence on phase diagrams of the nanosystem are studied. Thus, the magnetic properties of the system such as the critical temperature, the magnetization, and the coercive field are computed.