Series expansions for a Heisenberg antiferromagnetic model forSrCu2(BO3)2

We use a variety of series expansion methods at both zero and finite temperature to study an antiferromagnetic Heisenberg spin model proposed recently by Miyahara and Ueda for the quasi-two-dimensional material ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2.$ We confirm that this model exhibits a first-order quantum phase transition at $T=0\mathrm{}$ between a gapped dimer phase and a gapless Néel phase when the ratio ${x=J}^{\prime }/J$ of nearest- and next-nearest-neighbor interactions is varied, and locate the transition at $x_c=0.691\mathrm{}\left(6\right).$ Using longer series we are able to give more accurate estimates of the model parameters by fitting to the high-temperature susceptibility data.