2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/22345A novel variational method is proposed for calculating the percolation threshold, the real-space structure, and the thermodynamical compressibility of a disordered two-dimensional electron liquid. Its high accuracy is verified against prior numerical results and newly derived exact asymptotics. The inverse compressibility is shown to have a strongly asymmetric minimum at a density that is approximately the triple of the percolation threshold. This implies that the experimentally observed metal-insulator transition takes place well before the percolation point is reached.4 pages, 2 figures. (v2) minor changes (v3) reference added (v4) few more references addedMesoscale and Nanoscale Physicstext