Phase transitions for N-electron atoms at the large-dimension limit

Abstract

Symmetry breaking of electronic structure configurations for N-electron atoms in weak magnetic and electric fields at the large-dimension limit is described in terms of standard phase transitions. This symmetry breaking, which leads to ionization, is completely analogous to phase transitions and critical phenomena in statistical mechanics. This analogy is shown by allowing the nuclear charge to play a role analogous to temperature in statistical mechanics. For the exact solution of N-electron atoms at the large-dimension limit, the symmetry breaking is shown to be a first-order phase transition. For the special case of two-electron atoms, the first-order transition shows a triple point where three phases with different symmetry coexist. Treatment of the Hartree-Fock solution reveals a different kind of symmetry breaking where second-order phase transitions exist for N=2. We show that Hartree-Fock two-electron atoms in a weak external electric field exhibit a critical point with mean field critical exponents (\ensuremath{\mathrm{B}}=, \ensuremath{\alpha}=${0}_{\mathrm{dis}}$, \ensuremath{\delta}=3, and \ensuremath{\gamma}=1).