Table 1 The critical exponents of graphene related to the two-body charge density distribution function with their definitions.

From: Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions

Exponent

Definition

Closest fractional amount

a G

\({G}_{x}(R)\propto {a}_{G}\,\mathrm{log}(R)\)

\(\tfrac{1}{3}\)

τ G

\({G}_{x}({R}_{{\rm{\max }}})\propto {\zeta }^{-{\tau }_{G}}\)

\(\tfrac{7}{2}\)

τ R

\({R}_{{\rm{\max }}}\propto {\zeta }^{-{\tau }_{R}}\)

2

τ δ

\(\delta \propto {\zeta }^{-{\tau }_{\delta }}\)

τG/2

\({\tau }_{\tilde{G}}\)

\({\alpha }^{2}\tilde{G}(q=0)\propto {\zeta }^{-{\tau }_{\tilde{G}}}\)

\(\tfrac{9}{2}\)

τ q

\({\alpha }^{-1}{q}_{0}\propto {\zeta }^{{\tau }_{q}}\)

\(\tfrac{1}{2}\)

γ δ, R

\(\delta \propto {R}_{{\rm{\max }}}^{{\gamma }_{\delta ,R}}\)

\(\tfrac{1}{2}\)