Critical Phenomena for Electronic Structure at the Large-Dimension Limit

We show that the symmetry breaking of the electronic structure configurations at the large-D limit is completely analogous to the standard phase transitions and critical phenomena in statistical mechanics. Electronic structure at the large-D limit exhibits critical points with mean field critical exponents ( $\beta =\frac{1}{2}$, $\alpha {=0\mathrm{}}_{\mathrm{dis}}$, $\delta =3\mathrm{}$, and $\gamma =1\mathrm{}$). The complete mapping is presented for the Hartree-Fock two-electron atom in weak electric field and the two Coulomb center problems.