Coopersmith inequality. Exponents phi,psi

LagrangeEuler

Coopersmith inequality is defined for [tex]T=T_c[/tex], [tex]H\rightarrow 0[/tex]

[tex]M\sim H^{\frac{1}{\delta}}[/tex]

2 question

1. Introduce the exponents [tex]\phi[/tex] and [tex]\psi[/tex].

[tex]C_H\sim H^{-\phi}[/tex]
[tex]S(H)\sim -H^{\psi}[/tex]

Why we shoot with that form?

2. Why minus in second relation?
[tex]S(H)\sim -H^{\psi}[/tex]