Study of cell distribution functions of the three-dimensional Ising model

The single and joint distribution functions of the nearest-neighbor cell magnetization of the three-dimensional Ising model have been studied by Monte Carlo methods. Near the critical point, both distribution functions tend, for large $L$, towards scaled universal forms. Estimates of the order parameter and susceptibility are obtained from the distribution functions. The critical temperature is estimated by a method independent of the estimate of the critical exponents. The critical exponent $\nu$ is obtained with the use of finite-size scaling arguments. The joint distribution function shows a double-well structure for $T<\mathrm{}{T}_c$ and can be represented by a coarse-grained effective Hamiltonian of two cell variables. We have determined the dependence of this functional on the coarse-graining cell size for several temperatures. In particular, we have calculated the dependence of the "spinodal curve" on the (scaled) coarse-graining size. The relevance of this work to the kinetics of first-order phase transitions is also discussed.