Thermal and hysteretic magnetic properties of La2/3Ca1/3MnO3 nanoparticles were studied using Monte Carlo simulations, with emphasis on the influence of anisotropy. In this work, several nanoparticle sizes ranging from 2.32 to 11.58nm were analyzed and their properties were compared to those of the bulk material. The magnetic behavior of the material was modeled using the three dimensional Heisenberg model with nearest neighbor interactions. Furthermore, both uniaxial and Néel anisotropies were considered for core and surface magnetic sites respectively. Deviations in the critical temperature and coercive field were observed for nanoparticles when compared with those of the bulk material. In addition to these properties, the special spin configurations that arise from the competition between the exchange, anisotropy and external magnetic field were also studied. All these effects are interpreted in terms of the surface properties such as the Néel anisotropy and the decrease in the coordination number.