New parameters to characterize the nematic transition for rods deposition on 2D lattices

We tackle the problem of excluded volume deposition of rigid rods of length k unit cells over square lattices. Two new features are introduced: a) two new short-distance complementary order parameters (called Π and Σ) are defined, used and discussed to deal with the phases present as coverage increases; b) the interpretation is now done beginning at the high-coverage locally ordered phase (present regardless of the k value) which allows to interpret the low coverage nematic phase as an ergodicity breakdown present for k ≥ 7. In addition data analysis is now done by a combination of mutability (dynamical information theory method) and Shannon entropy (static distribution analysis). Moreover, a comparison between mutability and Shannon entropy is done reporting their advantages and disadvantages for dealing with this problem. Parameter Π turns out to better characterize this system through the entire parameter space.