New parameters for an alternative characterization of the nematic transition for rods deposition on 2D lattices

The problem of excluded volume deposition of rigid rods of length k unit cells over square lattices is revisited. Two new features are introduced: a) two new short-distance complementary order parameters (called Π and Σ) are defined, calculated 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 offers also some novelty as both mutability (dynamical information theory method) and Shannon entropy (static distribution analysis) will be invoked to further characterize the phases. Moreover, mutability and Shannon entropy are compared between themselves reporting their advantages and disadvantages for dealing with this problem. The advantages of parameter Π over any other parameter is also established.