  We study a p-spin spin-glass model to understand if the finite-temperature
glass transition found in the mean-field regime of p-spin models, and used to
model the behavior of structural glasses, persists in the non-mean-field
regime. By using a 3-spin spin-glass model with long-range power-law diluted
interactions we are able to continuously tune the (effective) space dimension
via the exponent of the interactions. Monte Carlo simulations of the spin-glass
susceptibility and the two-point finite-size correlation length show that deep
in the non-mean-field regime the finite-temperature transition is lost, whereas
this is not the case in the mean-field regime, in agreement with the prediction
of Moore and Drossel [Phys. Rev. Lett. 89, 217202 (2002)] that 3-spin models
are in the same universality class as an Ising spin glass in a magnetic field.
However, slightly in the non-mean-field region, we find an apparent transition
in the 3-spin model, in contrast to results for the Ising spin glass in a
field. This may indicate that even larger sizes are needed to probe the
asymptotic behavior in this region.
