Magnetic properties of nanosized systems, discrete and continuum approaches*

In this work we present results obtained with a scaled Monte Carlo technique in two systems: The first one is the system proposed at the NIST web page and known as the $\mu $MAg Standard Problem No 3. There, the system is a perfect cube made of a magnetic material, with uniaxial anisotropy and the problem is to find the critical edge length at which the magnetic vortex structure and the most uniform arrangement of magnetization (the so-called flower state) are of equal energy. The second system is a study of the reversion process in an ideally soft magnetic nanowire of cylindrical shape, (diameter of 60nm and 1$\mu $m length) at room temperature. By calculating magnetic energies, using continuum and exact methods, in a simple one dimensional discrete system, we show that the usual scaling technique used in some micromagnetic models breaks down at the nanometer scale.