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Precise determination of the low-energy electronuclear Hamiltonian of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">LiY</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>โ</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ho</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">F</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>
The insulating rare-earth magnet ${\mathrm{LiY}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}{\mathrm{F}}_{4}$ has received great attention because a laboratory field applied perpendicular to its crystallographic $c\phantom{\rule{0.28em}{0ex}}\mathrm{axis}$ converts the low-energy electronic spin Hamiltonian into the (dilute) transverse field Ising model. The mapping between the real magnet and the transverse field Ising model is strongly dependent on the exact โฆ