SciPost Submission Page
Spin models from nonlinear cellular automata
by Konstantinos Sfairopoulos, Luke Causer, Jamie F. Mair, Stephen Powell, Juan P. Garrahan
Submission summary
| Authors (as registered SciPost users): | Konstantinos Sfairopoulos |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.19572v3 (pdf) |
| Data repository: | https://zenodo.org/records/17492872 |
| Date submitted: | Oct. 31, 2025, 7:21 p.m. |
| Submitted by: | Konstantinos Sfairopoulos |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
We study classical and quantum spin models derived from one-dimensional cellular automata (CA) with nonlinear update rules, focusing on rules 30, 54 and 201. We argue that the classical models, defined such that their ground states correspond to allowed trajectories of the CA, are frustrated and can be described in terms of local defect variables. Including quantum fluctuations through the addition of a transverse field, we study their ground state phase diagram and quantum phase transitions. We show that the nonlinearity of the CA rule leads to a quantum order-by-disorder mechanism, which selects a particular (rule-dependent) spatial structure for small transverse fields, with spontaneous breaking of the translation symmetry in some cases. Using numerical results for larger fields, we also observe a first-order quantum phase transition into a quantum paramagnet, as in previous studies of spin models based on linear CA rules.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block