## Gap exponents

Gap exponents are denoted like critical exponents for higher derivatives of Gibbs potential.
$$\Delta_l'$$
$$(\frac{\partial G}{\partial H})_T=G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta_1'}G^{0}$$

$$(\frac{\partial^l G}{\partial H^l})_T=G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta_l'}G^{l-1}$$

$$\alpha'$$ is critical exponent for heat capacity. People used that
$$G^{0}\propto (1-\frac{T}{T_c})^{2-\alpha'}$$

How to get that? Why gap exponents are important?
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 Because I still didn't find answer for my question I will write here more details. So ##G(T,H)## is Gibbs thermodynamics potential. Derivatives of Gibbs potential are defined by $$(\frac{\partial G}{\partial H})_T \equiv G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta'_1}G^{(0)}$$ $$(\frac{\partial G^{2}}{\partial H^{2}})_T \equiv G^{(2)}\propto (1-\frac{T}{T_c})^{-\Delta'_2}G^{(1)}$$ $$...$$ $$(\frac{\partial G^{l}}{\partial H^{l}})_T \equiv G^{(l)}\propto (1-\frac{T}{T_c})^{-\Delta'_l}G^{(l-1)}$$ Quontities ##\Delta'_l## are called gap exponents. In eqns ##H=0, T\rightarrow T^{+}_c##. $$G^{(1)} \propto M \propto (1-\frac{T}{T_c})^{\beta}$$ but that is for ##H=0, T\rightarrow T_c^{-}##. That is first conceptual problem. ##T\rightarrow T_c^{+}## or ##T\rightarrow T_c^{-}##.