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A novel variational method is proposed for calculating the percolationthreshold, the real-space structure, and the thermodynamical compressibility ofa disordered two-dimensional electron liquid. Its high accuracy is verifiedagainst prior numerical results and newly derived exact asymptotics. Theinverse compressibility is shown to have a strongly asymmetric minimum at adensity that is approximately the triple of the percolation threshold. Thisimplies that the experimentally observed metal-insulator transition takes placewell before the percolation point is reached.Comment: 4 pages, 2 figures. (v2) minor changes (v3) reference added (v4) few  more references adde

Nonlinear screening and percolative transition in a two-dimensional electron liquid