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A Monte Carlo simulation study of the exchange bias properties in ferromagnetic/antiferromagnetic (FM/AFM) bilayers by using a classical Heisenberg model and the Metropolis algorithm is addressed. In our model several contributions including nearest neighbors exchange interactions, two different interface couplings, magnetocrystalline anisotropy, and a Zeeman term were considered. Our study focuses on the influence of FM and AFM layer thicknesses (dF and dA ) on hysteresis loops, particularly exchange bias field (HEB) and coercive force (Hc) . Results reveal that the influence of dA on the exchange bias phenomenon is negligible, while dF produces an important effect on HEB and Hc. Such behaviors agree with several models and results reported in the literature. Concretely, our model allows inferring a dependence of the exchange bias field with the FM layer thickness proportional to 1/(dF)m characterized by an exponent m = 0.71plusmn0.11. On the other hand, coercive force exhibits a power law increase with the FM layer thickness when thermal fluctuations become relevant. For completeness, thermal stability of the hysteretic properties is finally presented and discussed.