Alternative characterization of the nematic transition in deposition of rods on two-dimensional lattices

Abstract

We revisit 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 and , 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 ordered phase which allows us to interpret the low-coverage nematic phase as an ergodicity breakdown present only when k 7. In addition the data analysis invokes both mutability (dynamical information theory method) and Shannon entropy (static distribution analysis) to further characterize the phases of the system. Moreover, mutability and Shannon entropy are compared, and we report the advantages and disadvantages they present for their use in this problem.

Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model

“…Data compressor wlzip was created to recognize repeated meaningful information in any data sequence [28][29][30][31][32][33][34][35][36][37]. It is offered free of charge upon request by email (eugenio.vogel@ufrontera.cl).…”

“…Actually, wlzip is less efficient than other compressors in terms of the final size achieved by the compressed file. However, compression done by wlzip is based on exact matching of data structures that correspond to properties of the system [28][29][30][31][32][33][34][35][36][37]. A high degree of compression is due to repetitive information characterizing a system that tends to preserve its properties within the time window under consideration.…”

The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice

“…al. by using an interesting new measure to study the Monte Carlo data [17,18]. The size of the file storing the time series of configurations is reduced in size using a zipping program.…”

Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices

“…There is some indication of the high density phase having power law correlations [46] with the second transition being in the non-Ising universality class [46,52], while the exact solution of soft repulsive rods on a tree-like lattice [53] suggests otherwise. More recently, the transitions in two dimensions have been studied using measures such as entanglement entropy, mutability, Shannon entropy and data compression [52,54,55].…”