SCOZA critical exponents and scaling in three dimensions

Abstract

The critical behavior of a self-consistent Ornstein–Zernike approach (SCOZA) that describes the pair correlation function and thermodynamics of a classical fluid, lattice gas, or Ising model is analyzed in three dimensions below the critical temperature, complementing our earlier analysis of the supercritical behavior. The SCOZA subcritical exponents describing the coexistence curve, susceptibility (compressibility), and specific heat are obtained analytically ( β=7/20, γ′=7/5, α′=−1/10 ). These are in remarkable agreement with the exact values ( β≈0.326, γ′≈1.24, α′≈0.11 ) considering that the SCOZA uses no renormalization group concepts. The scaling behavior that describes the singular parts of the thermodynamic functions as the critical point is approached is also analyzed. The subcritical scaling behavior in the SCOZA is somewhat less simple than that expected in an exact theory, involving two scaling functions rather than one.