Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices

Abstract

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, i.e., J(r)∼−Alnr in d=2 and J(r)∼A/r in d=3. This arises naturally as the T→0 limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets in checkerboard, SCGO, and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of A in both d=2 and d=3. In d=2, using the lattice-Green-function-based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphans), we find evidence that freezing into a glassy state occurs only in the limit of strong coupling, A=∞, while no such transition seems to exist in d=3. We also demonstrate the presence and importance of screening for such a magnet. We analyze the spectrum of the Euclidean random matrices describing a Gaussian version of this problem and identify a corresponding quantum mechanical scattering problem.