Gaussian critical exponent
= Gaussian critical exponent
{c}
{title2=$\alpha=2-d/2,\quad\Delta=(d+2)/4$}
For quadratic dispersion $p^2+t$ with no interacting anomalous dimension, the thermal and uniform-source scaling eigenvalues are $y_t=2$ and $y_h=(d+2)/2$. The generic homogeneous singular <free-energy density> has $2-\alpha=d/2$ and gap exponent $\Delta=(d+2)/4$. These Gaussian-model values below the upper critical dimension are not the exponents of an interacting scalar critical point.