  The nature of the interplay between fluctuations and quenched random disorder
is a long-standing open problem, particularly in systems with a continuous
order parameter. This lack of a full theoretical treatment has been underscored
by recent advances in experiments on charge density wave materials. To address
this problem, we formulate an exactly solvable model of a two-dimensional
randomly pinned incommensurate charge density wave, and use the large-$N$
technique to map out the phase diagram and order parameter correlations. Our
approach captures the physics of the Berezinskii-Kosterlitz-Thouless phase
transition in the clean limit at large $N$. We pay particular attention to the
roles of thermal fluctuations and quenched random field disorder in destroying
long-range order, finding a novel crossover between weakly- and
strongly-disordered regimes.
