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An ongoing problem in the study of a classical many-body system is thecharacterization of its equilibrium behaviour by theory or numericalsimulation. For purely repulsive particles, locating the melting line in thepressure-temperature plane can be especially hard if the interparticlepotential has a softened core or contains some adjustable parameters. A methodis hereby presented that yields reliable melting-curve topologies withnegligible computational effort. It is obtained by combining the Lindemannmelting criterion with a description of the solid phase as an elasticcontinuum. A number of examples are given in order to illustrate the scope ofthe method and possible shortcomings. For a two-body repulsion of Gaussianshape, the outcome of the present approach compares favourably with the moreaccurate but also more computationally demanding self-consistent harmonicapproximation.

On the accuracy of the melting curves drawn from modelling a solid as an elastic medium