[2] The Hohenberg-Kohn theorems, formulated by Hohenberg and Walter Kohn gave rise to the density functional theory (DFT) [3].
In 2004 he became Senior Vice Provost of Research at New York University, a position held until 2011, when he stepped down to join the Physics Department as Professor.
He became famous primarily for his investigations in the 1960s and 1970s in the theory of dynamic (i.e. temporally variable) critical phenomena close to phase transitions.
Additionally, Hohenberg worked (with Swift) on hydrodynamic instabilities, on the Swift–Hohenberg equation and on pattern formation in non-equilibrium systems with Michael Cross.
Preceding David Mermin and Herbert Wagner he proved in 1967 the impossibility of spontaneous symmetry breaking in one and two dimensions, now known as the Hohenberg–Mermin–Wagner theorem.