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- W4386840132 abstract "We show how the trajectories of $d$-dimensional cellular automata (CA) can be used to determine the ground states of $(d+1)$-dimensional classical spin models, and we characterise their quantum phase transition, when in the presence of a transverse magnetic field. For each of the 256 one-dimensional elementary CA we explicitly construct the simplest local two-dimensional classical spin model associated to the given CA, and we also describe this method for $d>1$ through selected examples. We illustrate our general observations with detailed studies of: (i) the $d=1$ CA Rule 150 and its $d=2$ four-body plaquette spin model, (ii) the $d=2$ CA whose associated model is the $d=3$ square-pyramid plaquette model, and (iii) two counter-propagating $d=1$ Rule 60 CA that correspond to the two-dimensional Baxter-Wu spin model. For the quantum spin models, we show that the connection to CAs implies a sensitivity on the approach to the thermodynamic limit via finite size scaling for their quantum phase transitions." @default.
- W4386840132 created "2023-09-19" @default.
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- W4386840132 date "2023-09-14" @default.
- W4386840132 modified "2023-09-27" @default.
- W4386840132 title "Cellular automata in $d$ dimensions and ground states of spin models in $(d+1)$ dimensions" @default.
- W4386840132 doi "https://doi.org/10.48550/arxiv.2309.08059" @default.
- W4386840132 hasPublicationYear "2023" @default.
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