Several systems have recently been demonstrated to show "non-Landau-Ginzburg-Wilson" quantum phase transitions, with different orderings on two sides of a continuous transition. We present two examples of classical statistical systems --- spin ice in a [100] magnetic field and an ordering transition of close-packed dimers on a cubic lattice --- that appear to show continuous (second-order) transitions that lie outside the Landau paradigm.

In both cases, strong local constraints mean that neither of the neighboring phases can be understood as thermally disordered, excluding the standard route to a continuum critical theory. Instead, we derive critical theories for both transitions by mapping from three-dimensional classical problems to two-dimensional quantum problems. For the dimer model, this mapping provides a direct connection to previous work on non-LGW transitions of lattice bosons at fractional filling factors.