  We study the critical breakdown of two-dimensional quantum magnets in the
presence of algebraically decaying long-range interactions by investigating the
transverse-field Ising model on the square and triangular lattice. This is
achieved technically by combining perturbative continuous unitary
transformations with classical Monte Carlo simulations to extract high-order
series for the one-particle excitations in the high-field quantum paramagnet.
We find that the unfrustrated systems change from mean-field to
nearest-neighbor universality with continuously varying critical exponents,
while the system remains in the universality class of the nearest-neighbor
model in the frustrated cases independent of the long-range nature of the
interaction.
