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The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t) ^d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeL ^d of the system. This lack of self-averaging is tested for both the Ising model and the φ⁴ model on the square lattice. Both models exhibit the same lawl(t)=(Rt) ^x withx=1/2, although the φ⁴ model has “soft walls”. However, spurious results withx≷1/2 are obtained if “bad” pseudorandom numbers are used, and if the numbern of independent runs is too small (n itself should be of the order of 10³). We also predict a critical singularity of the rateR∝(1−T/T _c) ^v(z−1/x),v being the correlation length exponent,z the dynamic exponent.

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