Fast simulation of the king model using cellular automata
H J Hemnann · 1991
A t~ml~stic lsmg cellular automaton (IC+.) IS proposed whlch can reproduce the thermodynamics of the king model. The automaton mle~ are preset tn lhe usual way but some random mixing of these existing mles is subsequently permitted. The model employs a vectonzed multispin coding algorithm to reach spin updating speeds comparable with the best Metmpolis Monte Carlo performances and IS charanenred by a nonlineardynami- cal cnticsl exponent whose value seems less than two Since the ising model and its variants are used to describe many critical phenomena, it is a challenge to discover faster algorithms for its simulation. Deterministic cellular automata have been considered as suitable candidates because the fact that no random numbers must be generated at each step makes them very efficient. The state of a spin is determined from the state of its neighbours on the basis of quenched rules which are determined at the Ftart of the simulation. One such cellular automaton is the Q2R (l-31. QZR automata have been studied extensively and these studies have revealed some difficulties with reproducing properly all the thermodynamic properties of king systems (3-5).