Classical Spin Liquid on the Maximally Frustrated Honeycomb Lattice

We show that the honeycomb Heisenberg antiferromagnet with J_{1}/2=J_{2}=J_{3}, where J_{1}, J_{2}, and J_{3} are first-, second-, and third-neighbor couplings, respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with nonmagnetic ions, fractionalized degrees of freedom carrying 1/3 of the free moment emerge. Their effective description in the limit of low temperature is that of spins randomly located on a triangular lattice, with a frustrated sublattice-sensitive interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder. This comes with a clear experimental diagnostic in neutron scattering, which turns out to apply also to the case of the celebrated planar order by disorder of the kagome Heisenberg antiferromagnet.