  We propose discrete random-field models that are based on random partitions
of $\mathbb{N}^2$. The covariance structure of each random field is determined
by the underlying random partition. Functional central limit theorems are
established for the proposed models, and fractional Brownian sheets, with full
range of Hurst indices, arise in the limit. Our models could be viewed as
discrete analogues of fractional Brownian sheets, in the same spirit that the
simple random walk is the discrete analogue of the Brownian motion.
