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AbsiraeiWe develop a finite-suemaling theory describing the joint density and energy fluctuations in a near-mitical fluid. As a result of the mixing of the lemperalure and chemical potential in the WO relevant scaling fields, the energy operator features in the crilical density distribution as an antisymmetric mrrestion lo the Limiting ale-invariant form Both the limiling form and the correction am predicted to be fuaetions that are characteristic of lhe king universality dass, and am independently knom. The theory is tested with extensive Monte Carlo studies of lhe lvmdimensional LennardJones fluid, within the grand canonical ensemble. The simulations and sgling framework together are shown to prwide a powerful way of identifying lhe loCalion of lhe liquid-gas aitical point, while confirming and darimng its esenlially king charader. 'Ihe simulations also show a clearly identifiable signature of the rield-mixing responsible for the hilure of ihe law of rectilinear dismeler.

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We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.