SCOZA critical exponents and scaling in three dimensions

The critical behavior of a self-consistent Ornstein-Zernike approach (SCOZA ) that describes the pair correlation function and thermodynamics of a clas sical fluid, lattice gas, or Ising model is analyzed in three dimensions be low the critical temperature, complementing our earlier analysis of the sup ercritical behavior. The SCOZA subcritical exponents describing the coexist ence curve, susceptibility (compressibility), and specific heat are obtaine d analytically (beta=7/20, gamma'=7/5, alpha'=-1/10). These are in remarkab le agreement with the exact values (beta approximate to 0.326, gamma' appro ximate to 1.24, alpha' approximate to 0.11) considering that the SCOZA uses no renormalization group concepts. The scaring behavior that describes the singular parts of the thermodynamic functions as the critical point is app roached is also analyzed. The subcritical scaling behavior in the SCOZA is somewhat less simple than that expected in an exact theory, involving two s caling functions rather than one. (C) 2000 Elsevier Science B.V. All rights reserved.