  We study the Heisenberg model on the pinwheel distorted kagome lattice as
observed in the material Rb_2Cu_3SnF_12. Experimentally relevant thermodynamic
properties at finite temperatures are computed utilizing numerical
linked-cluster expansions. We also develop a Lanczos-based, zero-temperature,
numerical linked cluster expansion to study the approach of the pinwheel
distorted lattice to the uniform kagome-lattice Heisenberg model. We find
strong evidence for a phase transition before the uniform limit is reached,
implying that the ground state of the kagome-lattice Heisenberg model is likely
not pinwheel dimerized and is stable to finite pinwheel-dimerizing
perturbations.
