Recoverable systems and the maximal hard-core model on the triangular lattice
Combinatorics
2026-04-16 v2 Discrete Mathematics
Information Theory
math.IT
Probability
Abstract
In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice . The following results are obtained: (1) We derive bounds on the capacity of the associated recoverable system on ; (2) We show non-uniqueness of Gibbs measures in the high-activity regime; (3) We characterize extremal periodic Gibbs measures for sufficiently low values of activity.
Keywords
Cite
@article{arxiv.2602.18310,
title = {Recoverable systems and the maximal hard-core model on the triangular lattice},
author = {Geyang Wang and Alexander Barg and Navin Kashyap},
journal= {arXiv preprint arXiv:2602.18310},
year = {2026}
}
Comments
v2: Improved bound on the activity above which multiple phases occur in the high-activity regime. Extended abstract of this paper appears in Proc. 2026 IEEE International Symposium on Information Theory