  We revisit the seminal 1968 proof of the absence of crystalline order in two
dimensions and analyze the importance played in the quantum theorem by the
assumption of local pair potentials. We relax the assumption of local
potentials and consider instead nonlocal pair potentials. We show that the
1/k2-singularity that occurs in the Bogoliubov inequality, which leads to no
crystalline order in two dimensions for local potentials and nonzero
temperatures, does not occur for nonlocal potentials. Accordingly, crystalline
order in one and two dimensions cannot be ruled out for nonlocal pair
potentials at finite temperatures.
