  In critical lattice models, distance ($r$) dependent correlation functions
contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an
underlying continuum field theory. In Monte Carlo simulations and other
numerical approaches, the leading dimensions can be extracted by data fitting,
which can be difficult when two or more powers contribute significantly. Here a
method utilizing covariance between multiple lattice operators is developed
where the $r$ dependent eigenvalues of the covariance matrix represent scaling
dimensions of individual field operators. The scheme is tested on symmetric
operators in the two-dimensional tricritical Blume-Capel model, where the two
relevant dimensions, as well as some irrelevant ones, are isolated along with
their corresponding eigenvectors. The method will be broadly useful in studies
of classical and quantum models at multicritical points and for targeting
irrelevant operators at simple critical (or multicritical) points.
