Abstract
The order-disorder transition in a binary fcc Ising-crystal with competing thermal and ballistic jumps, as is found e.g. under irradiation with high energy particles is studied by a Monte-Carlo technique. The state of order is characterized by a four-dimensional order parameter X the relative A-occupation of the four simple cubic sublattices (each consisting of Ω atoms) into which the fcc lattice may be decomposed. In a mean-field approximation, the transition rates w(X→X′) between neighbouring states of order can be found. By integrating a trajectory in the order parameter space stochastically, i.e. with a suitable Monte-Carlo-method, the respective probability P(X) each state of order Xcan be computed. For a large system this yields a stochastic potential \( \varphi \left( {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{X}}} \right) = \frac{1}{\Omega }{\text{ }}\log {\text{ }}P\left( {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{X}}} \right){\text{ }} \). The simulation algorithm is based on a method proposed some years ago by Gillespie [8], where one computes the probability for the system to leave its current state through a “reaction channel” μ, in our case a transition between two special sublattices, after a delay time r. Integration yields the total time in a certain state X, i.e. its probability.
Published Version
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