The authors derives weak dependence conditions as the natural generalization to random fields on notions developed by P. Doukhan and S. Louhichi [Stochastic Processes Appl. 84, 313–342 (1999; Zbl 0996.60020)]. Examples of such weakly dependent fields are also defined. In the context of a weak dependence coefficient series with arithmetic or geometric decay, the authors give explicit bounds in the Prokhorov metric for the convergence in the empirical central limit theorem. For random fields indexed by \({\mathbb Z}^d ,\) in the geometric decay case, rates have the form \(n^{-1/(8d+24)}L(n)\), where \(L(n)\) is a power of \(\log (n).\)