Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

TL;DR

This paper extends the transfer matrix method to analyze confined parallel hard squares, deriving exact results for the equation of state and structural transitions between fluid and solid-like phases in narrow pores.

Contribution

It introduces an exact transfer matrix approach for quasi-one-dimensional hard square systems with passing particles and multiple layers, revealing continuous structural transitions.

Findings

Identifies three structural regimes: one-layer fluid, two-layer fluid, and solid-like layered structure.

Shows no thermodynamic phase transition occurs during the structural change.

High-density phase features clustered two-layer arrangements broken by particles in the pore center.

Abstract

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between $\sigma$ and $3\sigma$ ( $\sigma$ is the side length of the square). The exact equation of state and the nearest neighbour distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e. no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.