- Research Article
4
- 10.1088/0305-4470/23/18/021
The checkerboard update Glauber model, cellular automata and Ising models
- Sep 21, 1990
- Journal of Physics A: Mathematical and General
- H Fried
The checkerboard update Glauber model for the one-dimensional Ising model is mapped onto a cellular automata model. This cellular automata model is found to be a special case of the well known (two-state) triangular cellular automata model. The author shows, therefore, that there exists a subspace of the full parameter space of the triangular cellular automata that obeys detailed balance. Using this result the shows that there are no phase transitions within the interior of the cubical parameter space of the triangular cellular automata model. He identifies a new line of critical points for the triangular cellular automata. This critical line is associated with the zero-temperature critical line of the one-dimensional Ising antiferromagnet in an external field. The critical properties of the checkerboard Glauber model are studied and are found to be identical to those of the single-spin update model. In addition, the correlations in the checkerboard Glauber model are found to exhibit a null-cone structure, similar to that found in relativity theory. This null-cone, which originates in the constraints imposed by the checkerboard update procedure, is found to be a general property of the triangular cellular automata model.
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