= Solution
At fixed zero field, $\partial_T=T_c^{-1}\partial_t$. Therefore, away from $t=0$ on either branch,
$$
c_{h,s}=-T\left(\frac{\partial^2 f_s}{\partial T^2}\right)_h
=-\frac{T}{T_c^2}(2-\alpha)(1-\alpha)g_{f,\pm}(0)s^{-\alpha}.
$$
Thus \b[the singular <heat capacity> has exponent $\alpha$]. An arbitrary analytic background must be added to obtain the full <heat capacity>. Vanishing branch <amplitudes> or the marginal case $\alpha=0$ need care: a finite jump is compatible with this power counting, while a logarithmic singularity requires a logarithmic refinement of the assumed homogeneous form.
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