= Gaussian free-energy logarithm at effective dimension two
{c}
{title2=$F_S\propto t\log t$}
For a quadratic determinant in two effective momentum dimensions, differentiating the <free-energy density> with respect to the squared mass $R$ gives a term proportional to $\log(\Lambda^2/R)$. Integration gives $F_S\propto R\log R$ after subtracting analytic terms. Its thermal power index is still 1, but a strictly homogeneous pure-power expression misses this logarithm. It is a Gaussian determinant resonance, distinct from interaction-generated logarithms at an upper critical dimension.
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