Three theorems in discrete random geometry
Geoffrey Grimmett
Probability Surveys 8 (2011) 403–441, arxiv

PrS erratum

Theorem 2.2: The lower bound of d for the connective constant assumes a stronger notion of vertex-transitivity than implied by the conditions of the theorem. The lower bound is not satisfied by the hexagonal lattice.

The best such lower bound known to the author is Theorem 1.1 of Grimmett/Li.