Trapping statistics in growing self-interacting self-Avoiding walks: Square versus honeycomb lattices

The growing self-Avoiding walk has been extensively studied, particularly in relation to whether it shares universality classes with equally weighted self-Avoiding walks. This study expands the understanding of growing self-interacting self-Avoiding walks and presents perspective on how lattice geometry and interaction strength interplay. We compare these walks on square and honeycomb lattices, and enhance the analysis of their decision points to deepen insights into the trapping effect in these models. The main numerical results uncover a minimum in the mean trapping length as the interaction strength varies for the honeycomb lattice, similar to what is known for the square lattice, and saturation effects in mean trapping lengths, as well as insights originating from the trap size.