Broken particle–hole symmetry in critical fluids

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Abstract
The quantitative validity of asymptotic particle–hole symmetry in a fluid at its liquid–vapor critical point is determined by means of the exact mapping of the fluid Hamiltonian onto that of an effective Landau–Ginzburg–Wilson model studied first by Hubbard and Schofield. A particular three-particle correlation of a reference fluid is identified as that which controls the breaking of liquid–vapor symmetry, as manifested in a linear mixing of the pure Ising-like scaling fields and a singularity in the coexistence curve diameter. The inherent smallness of the mixing coefficient in a pair-potential fluid is shown to reflect the weak density dependence of the second moment of the two-particle direct correlation function of the reference system. It is further demonstrated that three-body interactions of the Axilrod–Teller-type enhance the broken particle–hole symmetry found in a purely pairwise-additive Hamiltonian, and detailed calculations give diameter anomaly amplitudes which vary linearly with the fluid polarizability, in quantitative agreement with recent experiments.