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Down to the lowest temperatures reached, these spins show no order, suggesting a quantum spin liquid.","posed_since":"","precise":"At the $4/7$ commensurate density of the 2D solid 3He layer on preplated graphite, multiple-spin ring exchange on a triangular lattice produces no magnetic order: magnetization measured by direct nuclear demagnetization rises smoothly down to about $1e-5\\,\\mathrm{K}$, which bounds any spin gap below about $1e-5\\,\\mathrm{K}$ (Masutomi et al. 2004). Determine the ground state of the triangular ring-exchange model at the measured $J2, J4, J5, J6$ ratios and test experimentally whether the state is a gapless spin liquid, gapped, or ordered. An answer is a classification supported by both computation and data below $1e-5\\,\\mathrm{K}$.","problem_ref":null,"references":"","settled_by":"Heat capacity and susceptibility below 1e-5 K together with a controlled numerical solution of the ring-exchange model at the measured couplings.","status_note":"","title":"Is second-layer 3He on graphite a gapless spin 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