= Scaling hypothesis for critical phenomena
{title2=$F_s(t,h)=\ell^{-D}F_s(\ell^{y_t}t,\ell^{y_h}h)$}
The scaling hypothesis treats the singular equilibrium <free-energy density> as a generalized homogeneous function of thermal and field-like scaling variables. Choosing the blocking factor to make the thermal variable order one gives $F_s=|t|^{D/y_t}f_\pm(h/|t|^{y_h/y_t})$. It concerns the singular contribution after subtracting analytic backgrounds. <Dangerously irrelevant couplings> or marginal logarithms can qualify this simple two-variable form. Differentiation yields <scaling relations for critical exponents>.
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