  We study a continuous quasi-two-dimensional order-disorder phase transition
that occurs in a simple model of a material that is inhomogeneously strained
due to the presence of dislocation lines. Performing Monte Carlo simulations of
different system sizes and using finite size scaling, we measure critical
exponents describing the transition of beta=0.18\pm0.02, gamma=1.0\pm0.1, and
alpha=0.10\pm0.02. Comparable exponents have been reported in a variety of
physical systems. These systems undergo a range of different types of phase
transitions, including structural transitions, exciton percolation, and
magnetic ordering. In particular, similar exponents have been found to describe
the development of magnetic order at the onset of the pseudogap transition in
high-temperature superconductors. Their common universal critical exponents
suggest that the essential physics of the transition in all of these physical
systems is the same as in our model. We argue that the nature of the transition
in our model is related to surface transitions, although our model has no free
surface.
