Digital dynamics and the simulation of magnetic systems

Abstract

This paper investigates the problems associated with simulating many-body systems with finite-state machines such as computers. It is shown that the digital (discrete) character of time brings in features which are not encountered in the usual analytical studies using continuous time. This is illustrated with a thorough study of the dynamics of simple magnetic systems with competing interactions. Whereas continuous dynamics, as derived from the usual master-equation approach, yields asymptotic behavior which is time independent, dynamics in digital time can lead to complex behavior characterized by the existence of multiple basins of attraction, broken symmetries, oscillations, and chaos. These results might provide a dynamical explanation for the breakdown of ergodicity which has been reported in Monte Carlo studies of spin-glasses.