A.K. Murtazaev - Dr. Sci. (Phys.-Math.), Professor, Corresponding Member RAS, Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala. E-mail: m_akai2005@mail.ru M.K. Ramazanov - Ph.D. (Phys.-Math.), Senior Research Scientist, Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala. E-mail: sheikh77@mail.ru M.K. Badiev - Ph.D. (Phys.-Math.), Senior Research Scientist, Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala. E-mail: m_zagir@mail.ru

Frustrated model of magnetic nanostructures are studied using the high-efficient replica Monte-Karlo algorithm. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r = J2/J1 in the value ranges r [0.0,0.4] and r [0.7,1.0] with Δr = 0.1. The static critical exponents of the heat capacity, the susceptibility, the ordering parameter, and the correlation length, as well as the Fisher exponent, are calculated by means of the finite-size scaling theory. The universality class of the critical behavior of this model is revealed to remain within the limits of values r [0.0,0.4]. It is found that the change in the next-nearest-neighbor interaction value in the range r [0.7,1.0] leads to nonuniversal critical behavior.

 

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