We present an adaptive algorithm for the optimal phase space sampling in Monte Carlo simulations of 3D Heisenberg spin systems. Based on a golden rule of the Metropolis algorithm which states that an acceptance rate of 50% is ideal to efficiently sample the phase space, the algorithm adaptively modifies a conebased spin update method keeping the acceptance rate close to 50%. We have assessed the efficiency of the adaptive algorithm through four different tests and contrasted its performance with that of other common spin update methods. In systems at low and high temperatures and anisotropies, the adaptive algorithm proved to be the most efficient for magnetization reversal and for the convergence to equilibrium of the thermal averages and the coercivity in hysteresis calculations. Thus, the adaptive algorithm can be used to significantly reduce the computational cost in Monte Carlo simulations of 3D Heisenberg spin systems.

In this work, Monte Carlo simulations based on metropolis algorithm were performed to study the critical and compensation temperatures of a core-shell nanowire with spins [Formula: see text] and [Formula: see text], respectively, considering an Ising antiferromagnetic system. The influence of nearest neighbors exchange interactions and crystal field anisotropy on the critical and compensation behaviors of the system has been analyzed. The effects of the nanowire height in the critical and compensation temperatures were evaluated. The results show that, for a system with given values of exchange interaction constants and crystal field anisotropy, a compensation point only appears if two requirements are satisfied. First, the weight of the core magnetization in the total magnetization must be greater than the weight of the shell magnetization at zero temperature. And second, the exchange constant of shell ions must be greater than a certain value. This value is, at the same time, greater than the exchange constant of core ions. The critical and compensation temperatures are very sensitive to variations in the exchange constant of the shell ions and core ions, respectively, while the crystal field anisotropy affects both temperatures.

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