We study the phase diagram and critical properties of quantum Ising
chains with long-range ferromagnetic interactions decaying in a
power-law fashion with exponent \alphaα,
in regimes of direct interest for current trapped ion experiments. Using
large-scale path integral Monte Carlo simulations, we investigate both
the ground-state and the nonzero-temperature regimes. We identify the
phase boundary of the ferromagnetic phase and obtain accurate estimates
for the ferromagnetic-paramagnetic transition temperatures. We further
determine the critical exponents of the respective transitions. Our
results are in agreement with existing predictions for interaction
exponents \alpha<1α>1
up to small deviations in some critical exponents. We also address the
elusive regime \alpha < 1α<1,
where we find that the universality class of both the ground-state and
nonzero-temperature transition is consistent with the mean-field limit
at \alpha = 0α=0.
Our work not only contributes to the understanding of the equilibrium
properties of long-range interacting quantum Ising models, but can also
be important for addressing fundamental dynamical aspects, such as
issues concerning the open question of thermalization in such
models.
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