Spatially correlated nuclei: How the Johnson-Mekl-Avrami-Kolmogorov formula is modified in the case of simultaneous nucleation

We present a theoretical investigation about the role played by spatial correlation among nuclei in the kinetics of first-order phase transitions. From the cluster expansion of the distribution functions in terms of the m-dots correlation functions, we obtain the equation which describes the kinetics in case of simultaneous nucleation. Truncation of the cluster expansion to the lowest order terms leads to an analytical solution. In order to test it we compare it to Monte Carlo simulations for the hard-core model, finding an excellent agreement. The theory is also applied to estimate the rate of random sequential adsorption of circular disks.