Title: Spin liquid and infinitesimal-disorder-driven cluster spin glass in the kagome lattice,
Abstract: The interplay between geometric frustration (GF) and bond disorder is studied
in the Ising kagome lattice within a cluster approach. The model considers
antiferromagnetic (AF) short-range couplings and long-range intercluster
disordered interactions. The replica formalism is used to obtain an effective
single cluster model from where the thermodynamics is analyzed by exact
diagonalization. We found that the presence of GF can introduce cluster
freezing at very low levels of disorder. The system exhibits an entropy plateau
followed by a large entropy drop close to the freezing temperature. In this
scenario, a spin-liquid (SL) behavior prevents conventional long-range order,
but an infinitesimal disorder picks out uncompensated cluster states from the
multi degenerate SL regime, potentializing the intercluster disordered coupling
and bringing the cluster spin-glass state. To summarize, our results suggest
that the SL state combined with low levels of disorder can activate small
clusters, providing hypersensitivity to the freezing process in geometrically
frustrated materials and playing a key role in the glassy stabilization. We
propose that this physical mechanism could be present in several geometrically
frustrated materials. In particular, we discuss our results in connection to
the recent experimental investigations of the Ising kagome compound
Co$_3$Mg(OH)$_6$Cl$_2$.