One can also solve for ϕ ϕ ( x ) , from which the scaling exponent, ν ν , for correlation length ξ ξ ∼ ∼ ( T − − T c ) − − ν ν can deduced. From these, the Ginzburg criterion for the upper critical dimension for the validity of the Ising mean-field Landau theory (the one without long-range correlation) can be calculated as: