Phase diagram of a bulk 1d lattice Coulomb gas

TL;DR

This paper uses transfer matrix methods to analyze the phase diagram of a one-dimensional lattice Coulomb gas, revealing complex phase behavior including ordered and disordered phases and a first order transition, with implications for ionic liquid capacitors.

Contribution

It provides the first detailed phase diagram of the bulk 1d lattice Coulomb gas using transfer matrix techniques, highlighting similarities to 3D systems.

Findings

Identifies a rich phase diagram with ordered and disordered phases.

Discovers a first order phase transition at low temperatures.

Shows the solid state at full packing can be ordered or disordered depending on temperature.

Abstract

The exact solution, via transfer matrix, of the simple one dimensional lattice Coulomb gas (1d LCG) model can reproduce peculiar features of ionic liquid capacitors, such as overscreening, layering, and camel- and bell-shaped capacitance curves. Using the same transfer matrix method, we now compute the bulk properties of the 1d LCG in the constant voltage ensemble. We unveil a phase diagram with rich structure exhibiting a low density disordered and high density ordered phases, separated by a first order phase transition at low temperature; the solid state at full packing can be ordered or not, depending on the temperature. This phase diagram, which is strikingly similar to its three dimensional counterpart, also sheds light on the behaviour of the confined system.