Theory and simulation
The investigation of single magnetic atoms and magnetic clusters with a spin-polarized scanning tunneling microscope (SP-STM) raises the necessity of a quantum mechanical description of spin systems. The components of a spin, whose expectation values can be measured with an SP-STM, can be represented as elements of a local -algebra .
A Monte Carlo simulation is a stochastic method, which relies on repeated random experiments. This method is mainly used, if it is impossible or infeasible to compute an exact result. The calculated observables are statistical averages, whose variance strongly depends on the number of performed random samplings.