Phase diagram of a bulk 1d lattice Coulomb gas

¹ PCT, UMR Gulliver 7083, ESPCI Paris and CNRS - 10 rue Vauquelin, F-75005 Paris, France
² Université de Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798 F-33400 Talence, France
³ Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana - SI-1000 Ljubljana, Slovenia
⁴ Department of Theoretical Physics, J. Stefan Institute - SI-1000 Ljubljana, Slovenia

Received: 23 November 2015
Accepted: 13 January 2016

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 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.