Dice Question Streamline Icon: https://streamlinehq.com

Admissible mosaics for pruned nonlinear field theories

Describe the set of admissible symbol mosaics for nonlinear lattice field theories with pruning, i.e., with couplings weaker than the anti-integrable limit, and characterize how admissibility changes with coupling strength.

Information Square Streamline Icon: https://streamlinehq.com

Background

Beyond the anti-integrable (strong-coupling) regime, nonlinear interactions prune the set of admissible configurations. Understanding this pruning at the level of symbolic mosaics is necessary for systematic enumeration of orbits in more realistic parameter regimes.

A grammar for pruned systems would enable efficient generation and weighting of periodic states across coupling ranges and connect symbolic dynamics with field-theoretic stability data.

References

At the present stage of development, our spatiotemporal theory of chaos leaves a number of open problems that we plan to address in future publications: Describe the admissible {mosaic}s of a nonlinear field theory with pruning, i.e., with couplings weaker than those topologically equivalent to the anti-integrable limit (see \refsect{s:mosaics} and companion paper III\rf{WWLAFC22}).

— A chaotic lattice field theory in two dimensions (2503.22972 - Cvitanović et al., 29 Mar 2025) in Subsection 'Open questions', Section 'Summary and open questions'