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Accurate phase diagrams of multicomponent plasmas are required for themodeling of dense stellar plasmas, such as those found in the cores of whitedwarf stars and the crusts of neutron stars. Those phase diagrams have beencomputed using a variety of standard techniques, which suffer from physical andcomputational limitations. Here, we present an efficient and accurate methodthat overcomes the drawbacks of previously used approaches. In particular,finite-size effects are avoided as each phase is calculated separately; theplasma electrons and volume changes are explicitly taken into account; andarbitrary analytic fits to simulation data are avoided. Furthermore, nosimulations at uninteresting state conditions, i.e., away from the phasecoexistence curves, are required, which improves the efficiency of thetechnique. The method consists of an adaptation of the so-called Gibbs-Duhemintegration approach to electron-ion plasmas, where the coexistence curve isdetermined by direct numerical integration of its underlying Clapeyronequation. The thermodynamics properties of the coexisting phases are evaluatedseparately using Monte Carlo simulations in the isobaric semi-grand canonicalensemble. We describe this Monte Carlo-based Clapeyron integration method,including its basic principles, our extension to electron-ion plasmas, and ournumerical implementation. We illustrate its applicability and benefits with thecalculation of the melting curve of dense C/O plasmas under conditions relevantfor white dwarf cores and provide analytic fits to implement this new meltingcurve in white dwarf models. While this work focuses on the liquid-solid phaseboundary of dense two-component plasmas, a wider range of physical systems andphase boundaries are within the scope of the Clapeyron integration method,which had until now only been applied to simple model systems of neutralparticles.

Direct Evaluation of the Phase Diagrams of Dense Multicomponent Plasmas by Integration of the Clapeyron Equations