Nonlinear cellular automata rules produce frustrated spin models whose quantum versions exhibit order-by-disorder and first-order phase transitions to paramagnets.
For this CA rule, we conjecture (but do not have a proof [72]) that there is a single configu- ration compatible with PBC for any odd L and three for any even L
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Spin models from nonlinear cellular automata
Nonlinear cellular automata rules produce frustrated spin models whose quantum versions exhibit order-by-disorder and first-order phase transitions to paramagnets.