A New Condition for the Invariance Principle for Stationary Random Fields

We establish a central limit theorem and an invariance principle for stationary random fields. In particular, we extend the Maxwell--Woodroofe condition on stationary processes to the multiparameter setting. Our result is obtained via an $m$-dependent approximation method. As applications, we improve known results on the invariance principles for orthomartingales and functionals of linear random fields.