Phase diagram and critical properties of Yukawa bilayers

TL;DR

This paper analyzes the phase diagram and critical properties of Yukawa bilayer systems, revealing detailed phase transitions, resolving longstanding controversies, and providing high-precision energy calculations using a novel lattice summation method.

Contribution

The study introduces a lattice summation method with generalized Misra functions for precise energy calculations, clarifies phase transition points, and characterizes critical lines in Yukawa bilayer systems.

Findings

Identifies the transition at η=0 between hexagonal phases.

Discovers a narrow continuous region in the rhombic phase.

Shows all second-order transitions are mean-field type.

Abstract

We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance $\eta$. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and L\"owen [Phys. Rev. Lett. 91 (2003) 146101], exhibits five different staggered phases as $\eta$ varies from 0 to intermediate values. We present a lattice summation method using the generalized Misra functions which permits us to calculate the energy per particle of the phases with a precision much higher than usual in computer simulations. This allows us to address some tiny details of the phase diagram. Going from the hexagonal phase I to phase II is shown to occur at $\eta=0$, which resolves a longtime controversy. We find a tricritical point where Messina and L\"owen suggested a coexistence domain of several phases which was suggested to divide the staggered rhombic phase into two separate regions. Our calculations reveal one continuous region for this rhombic phase with a very narrow connecting channel. Further we show that all second-order phase transitions are of mean-field type. We also derive the asymptotic shape of critical lines close to the Coulomb and hard-spheres limits. In and close to the hard-spheres limit, the dependence of the internal parameters of the present phases on $\eta$ is determined exactly.