  We calculate properties of dipolar interacting ultracold molecules or Rydberg
atoms in a semi-synthetic three-dimensional configuration -- one synthetic
dimension plus a two-dimensional real space optical lattice or periodic
microtrap array -- using the stochastic Green function Quantum Monte Carlo
method. Through a calculation of thermodynamic quantities and appropriate
correlation functions, along with their finite size scalings, we show that
there is a second order transition to a low temperature phase in which
two-dimensional `sheets' form in the synthetic dimension of internal rotational
or electronic states of the molecules or Rydberg atoms, respectively.
Simulations for different values of the interaction $V$, which acts between
atoms or molecules that are adjacent both in real and synthetic space, allow us
to compute a phase diagram. We find a finite-temperature transition at
sufficiently large $V$, as well as a quantum phase transition -- a critical
value $V_c$ below which the transition temperature vanishes.
