Mathematics & Physics 2017, 10(1), 128–131 УДК 539.2 Zeros in Partition Function and Critical Behavior of Disordered Three Dimensional Ising Model Andrey N.Vakilov∗ Omsk State University Mira, 55a, Omsk, 644077 Russia Received 10.08.2016, received in revised form 10.10.2016, accepted 14.11.2016 We used a Monte Carlo simulation of the structurally disordered three dimensional Ising model. <...> For the systems with spin concentrations p = 0.95, 0.8, 0.6 and 0.5 we calculated the correlation-length critical exponent ν by finite-size scaling. <...> The analysis of the results demonstrates the nonuniversality of the critical behavior in the disordered Ising model. <...> Keywords: Monte Carlo simulation, complex temperature, critical exponents, disordered systems,zeroes of the partition function. <...> The analysis of the effect of the structural disorder on second order phase transitions leads to the following two questions. <...> First, do the critical exponents of a “pure” magnetic system change at the dilution of it by nonmagnetic impurities? <...> Second, if they do change, are these new critical exponents universal, i.e., independent of the concentration of structural effects up to the percolation threshold? <...> It was shown that the critical exponents for the systems with quenched structural defects differ from those characteristic of similar systems without defects if the critical exponent for the specific heat in the pure system is positive. <...> This criterion is met only for three dimensional systems with the critical behavior described by the Ising model. <...> The critical behavior of dilute Ising-type magnetic systems was studied in [2–9] using the renormalization-group techniques, numerical Monte Carlo simulations, and experimental methods. <...> Currently, we have a positive answer to the question concerning the existence of the novel universality class for dilute Ising-type magnetic systems. <...> Model and observables We consider a model of disordered spin system in the form of a cubic lattice with linear size L under certain boundary conditions. <...> The microscopic Hamiltonian of the disordered Ising model can be written in the form H = −J ∑ <i,j> ∗vakilovan@omsu.ru ⃝ Siberian Federal University. <...> All rights reserved c – 128 – pipjSiSj, (1) Andrey N.Vakilov Zeros in Partition Function and Critical Behavior of Disordered Three Dimensional . . . where J is the short-range exchange interaction between spins Si fixed <...>