Finite size effects on the temperature dependence of the uniaxial magnetic anisotropy, longitudinal and transverse susceptibilities and specific heat are examined for L1 o -ordered FePt nanoparticles using an atomistic model based on an effective classical spin Hamiltonian. At low temperatures below criticality, we study the intrinsic uniaxial magnetic anisotropy energy (MAE) K 1 and its scaling with magnetization K 1 ðTÞ $ M s ðTÞ d and using Langevin dynamics simulations we show that the dependence of the exponent d on the size L and aspect ratio of the grain arises from decomposition of the MAE into bulk and surface dependent terms. Monte Carlo simulations in the critical regime near the Curie temperature T c , show that the temperature variation of the specific heat and longitudinal susceptibility is given by finite size scaling relations c ¼ L a=c ðL 1= Þ and v ¼ L c=ṽ ðL 1= Þ, respectively, where ¼ ðT À T c Þ=T c is the reduced temperature, and the susceptibility scaling functionṽ can be approximated by a Lorentzian. Our estimates of the critical exponents a; c, and appear to be in agreement with the universality class of the 3D Ising model. V C 2013 AIP Publishing LLC. [http://dx.