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• The critical temperature of FeNi and FePt alloys using Heisenberg interaction is closer to the experimental value than the Ising interaction. • The FeNi and FePt alloys prefer a ferromagnetic phase over the ferrimagnatic phase. • The Ising interaction predicts higher critical temperature for the FeNi alloy than the Heisenberg interaction. • The Heisenberg interaction predicts higher critical temperature for the FePt alloy than the Ising interaction. A Monte Carlo simulation has been used to explore the magnetic properties of L1 0 ordered FeNi and FePt binary alloys. Our Hamiltonians include Heisenberg interaction or Ising interaction. Our calculations of variations of specific heat C v , magnetic susceptibility χ and the magnetization M with the temperature T showed that predicted critical temperature for ferromagnetic phase is very close to the experimental values for these alloys. Also, thermal hysteresis loops, magnetic remanence, and the coercive field have been calculated. Moreover, the magnetic properties of the ferrimagnetic phase are presented. [ABSTRACT FROM AUTHOR]