Improved parameter bounds for applying Pirogov–Sinai theory

Improve the sufficient inequalities relating the inverse temperature, the Peierls constant, and the other model parameters so as to obtain sharper estimates for the high- and low-activity regimes in which Pirogov–Sinai theory applies to maximal hard-core models.

Background

The paper derives explicit sufficient conditions for the applicability of Pirogov–Sinai theory to maximal hard-core models. In the examples considered, these conditions yield very poor numerical estimates for the activity thresholds, despite proving crystallization in principle. The authors identify sharpening these inequalities as a concrete unresolved problem.