From 1984 to 1996, he was a member of the committee for human rights of the New York Academy of Sciences.
Hohenberg was a member of the American Academy of Arts and Sciences (since 1985), the National Academy of Sciences (from 1989), the American Philosophical Society (since 2014) and the New York Institute for the Humanities (since 2016).
He received in 1990 the Fritz London Prize, in 1999 the Max Planck Medal, and in 2003 the Lars Onsager Prize of the APS.
Hohenberg formulated in 1964 with Walter Kohn the Hohenberg-Kohn theorem in the course of his work on density functional theory.
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.
He collaborated thereby with Bertrand Halperin, Shang-keng Ma and Eric Siggia in the application of renormalization methods.
Additionally, Hohenberg worked (with Swift) on hydrodynamic instabilities and on pattern formation in non-equilibrium systems with Michael Cross.
Independently of Mermin and Wagner he proved in 1967 the impossibility of spontaneous symmetry breaking in one and two dimensions.
In collaboration with Richard Friedberg, he presented a new formulation of nonrelativistic quantum mechanics based on the consistent histories approach to the interpretation of quantum mechanics.
An accomplished continuous distance swimmer, Hohenberg in the second decade of the 21st century annually contested the artist/writer Richard Kostelanetz in a one-hour race at the NYU Coles pool until the pool was closed.
Usually they declare a draw.