Global Crossover Behaviour of Fluids

The equations presented in the preceding seetions deal with the thermodynamic behaviour of fluids in the near-critical region. For many applications one needs a global equation of state that not only incorporates the effects of critical fluctuations in the near-critical region, but also yields a representation of the thermodynamic properties of fluids over large ranges of temperatures and 

1 Switching from Scaled Equations to Classical Equations 

2 Crossover from Ising-like to Nonasymptotic Mean-Field Critical Behaviour 

The theory described in Section 10.5.1 accounts for the crossover from Ising-like critical behaviour to asymptotic mean-field critical behaviour. To extend the range of applicability one may consider crossover from Ising-like critical behaviour to nonasymptotic mean-field critical behaviour by including higher-order terms in the classical Landau expansion of eq 10.83  

Equation 10.92 contains an asymmetric term ocM that is not present in the (symmetric) Ising model or lattice gas. We note that in the mean-field approximation is of order t. Equation 10.85 for the renormalized potential Or now becomes  

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