Correlation lengths in quasi-one-dimensional systems via transfer matrices

TL;DR

This paper investigates the structural correlations in quasi-one-dimensional systems of hard disks and spheres using transfer matrix methods, revealing the theoretical basis for non-monotonic correlation length growth and structural crossovers observed in simulations.

Contribution

It introduces a theoretical framework linking eigenvalue crossings in transfer matrices to structural crossovers in correlation lengths.

Findings

Eigenvalue crossing explains correlation length kinks.

Structural crossovers are associated with eigenvalue splitting.

Theoretical results align with previous simulation observations.

Abstract

Using transfer matrices up to next-nearest-neighbour (NNN) interactions, we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders. Simulations have shown that the non-monotonic and non-smooth growth of the correlation length in these systems accompanies structural crossovers (Fu et al., Soft Matter, 2017, 13, 3296). Here, we identify the theoretical basis for these behaviour. In particular, we associate kinks in the growth of correlation lengths with eigenvalue crossing and splitting. Understanding the origin of such structural crossovers answers questions raised by earlier studies, and thus bridges the gap between theory and simulations for these reference models.