Wang-Landau study of lattice gases on geodesic grids
arXiv:2601.13397 · doi:10.1103/bnyl-k1mt
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 () 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.
arXiv comment13 pages, 21 figures
References in corpus (9)
- An efficient, multiple range random walk algorithm to calculate the density of states
- Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
- Stable Frank-Kasper phases of self-assembled, soft matter spheres
- Origin of similarity of phase diagrams in amphiphilic and colloidal systems with competing interactions
- Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers
- Self-assembled structures of colloidal dimers and disks on a spherical surface
- Combined density functional and Brazovskii theories for systems with spontaneous inhomogeneities
- Orientational ordering of lamellar structures on closed surfaces
- Aperiodic approximants bridging quasicrystals and modulated structures