Cellular automata as microcanonical simulators
P.M.C. de Oliveira, T. J. P. Penna, Suzana Maria Moss de Oliveira, Rita M. Zorzenon · Journal of Physics A Mathematical and General · 1991
The deterministic Q2R cellular automation has been tested by many authors as a fast algorithm to simulate the Ising model in the microcanonical ensemble. However, the magnetic susceptibility curve, measured from the fluctuations of the magnetization, is found to be far below the expected results inside the ordered Ising phase. The non-ergodicity degree of this automaton seems to be inadequate to simulate the Ising dynamics. In this work, the authors introduce two modified automata, and test their performance for the square lattice. For the first one, they found improved results concerning the Ising transition. For the second modified automaton the Ising transition does not occur, the magnetization vanishing even for energies far below the normal critical threshold. On the other hand, another transition appears at a different critical energy value that seems to be the same as that of the periodic-chaotic transition already observed in the normal Q2R dynamics. The critical indices of this new transition are measured from finite-size scaling, the results indicating that it is at the same universality class as the Ising transition.