Wang-Landau study of lattice gases on geodesic grids

TL;DR

This study uses Wang-Landau sampling to analyze lattice-gas systems on geodesic grids, revealing various low-temperature phases and structural motifs relevant for designing spherical templates.

Contribution

It introduces a detailed analysis of lattice gases on geodesic grids with multiple interaction patterns, providing exact statistical properties and phase characterization.

Findings

Identification of distinct low-temperature phases

Comparison of structural motifs with triangular lattice

Insights into designing spherical functional templates

Abstract

We study a family of lattice-gas systems defined on semiregular grids, obtained by projecting the vertices of three different geodesic icosahedra onto a spherical surface. By using couplings up to third neighbors we explore various interaction patterns, ranging from core-corona repulsion to square-well attraction and short-range attractive, long-range repulsive potentials. The relatively small number of sites in each grid ($\sim 100$) enables us to compute the exact statistical properties of the systems as a function of temperature and chemical potential by Wang-Landau sampling. For each case considered we highlight the existence of distinct low-temperature ``phases'', featuring, among others, regular-polyhedral, cluster-crystal, and worm-like structures. We highlight similarities and differences between these motifs and those observed on the triangular lattice under the same conditions. Finally, we discuss the relevance of our results for the bottom-up realization of spherical templates with desired functionalities.