  This paper establishes a central limit theorem and an invariance principle
for a wide class of stationary random fields under natural and easily
verifiable conditions. More precisely, we deal with random fields of the form
$X_k = g(\varepsilon_{k-s}, s \in \Z^d)$, $k\in\Z^d$, where
$(\varepsilon_i)_{i\in\Z^d}$ are i.i.d random variables and $g$ is a measurable
function. Such kind of spatial processes provides a general framework for
stationary ergodic random fields. Under a short-range dependence condition, we
show that the central limit theorem holds without any assumption on the
underlying domain on which the process is observed. A limit theorem for the
sample auto-covariance function is also established.
