ABSTRACT
The MC simulation technique with the implementation of the Metropolis algorithm [67-69] has been proved to be a very powerful tool for the systematic study of the magnetic behavior of nanoparticles and nanoparticle assemblies. It offers the possibility for atomic-scale treatment of nanoparticles in order to study details of their microstructure and the ability of the implementation of finite temperature. The MC simulation technique is a standard method to study models of equilibrium or nonequilibrium thermodynamic systems with many degrees of freedom by stochastic computer simulation. The starting point of the simulation is the appropriate choice of a model Hamiltonian and then the use of random numbers to simulate statistical fluctuations in order to generate the correct thermodynamical probability distribution according to a canonical ensemble [70]. In this way one may obtain microscopic information about complex systems that cannot be studied analytically or that might not be accessible in a real system. Contrary to Landau-Lifshitz or Langevin equations, the MC scheme provides a straightforward implementation of temperature. To simulate magnetic nanoparticles and nanoparticle assemblies and to derive thermodynamic averages, the elementary physical quantity that we use is the spin. In the case of single nanoparticles we consider a classical spin at each atomic site and we simulate using the MC technique the stochastic movement of the system in the phase space. In the case of assemblies of nanoparticles, we consider one or more effective spins for each nanoparticle, depending on its morphology to represent its magnetic state.
