[1] He is a fellow of the American Physical Society, nominated for "contributions to theoretical particle physics, including the seminal work on finite energy sum rules, research of the phenomenology of hadronic processes, and investigation of Hamiltonian lattice theories".

In 1974 he became the incumbent of the Edouard and Francoise Jaupart Chair of Theoretical Physics of Particles and Fields, a position he held until 2007.

After returning he was nominated Chairman of the Department of High Energy Physics (1984-1986), followed by tenures as Chairman of the School of Physics and Astronomy (1986-9),[8] Dean of the Raymond and Beverly Sackler Faculty of Exact Sciences (1990-1995), and first Director of the Adams Super Center for Brain Studies (1993-2000).

He was Chairman of the Israel Commission for High Energy Physics (1983-2003), and, in this capacity, served as an Israeli observer of the council of CERN (1991-2003).

[1] Horn's research work focused on theory and phenomenology of High Energy Physics until 1990.

[13] Moving to lattice gauge theories in 1979, he discovered, together with Shimon Yankielowic and Marvin Weinstein, a non-confining phase in Z(N) theories for large N.[14] In 1981 he demonstrated the existence of finite matrix models with link gauge fields,[15] nowadays known as quantum link models.

[17] Horn's contributions to neural modeling include a novel mechanism for memory maintenance via neuronal regulation in 1998, developed with Nir Levy and Eytan Ruppin[18] and unsupervised learning of natural languages in 2005, a joint work with Zach Solan, Eytan Ruppin and Shimon Edelman,[19] introducing novel algorithms for motif and grammar extraction from text.