Each ferromagnetic state, such as the single-domain (SD) state, has critical fields and grain sizes at which it becomes unstable. To determine the properties of these critical points, a three-dimensional numerical micromagnetic model is combined with nucleation theory. Isothermal hysteresis and grain growth are simulated for cuboids with no internal stress or magnetocrystalline anisotropy. Most jumps in hysteresis loops are turning points at which the susceptibility goes to infinity. The SD state becomes unstable at a pitchfork bifurcation, which has a jump in susceptibility but a continuous change in magnetic moment. This is a generalization of curling mode nucleation. As the grain size increases, there is an increasing gap in field between the curling mode nucleation and the first irreversible jump in magnetization. A similar gap is often seen experimentally between the formation of a small spike domain and the appearance of a full size body domain. For the first time in a micromagnetic simulation, minor branches are traced from the main hysteresis loop. When they occur, the main loop becomes wasp waisted. At any given grain size the lowest-energy state has SD-like stability in response to changes in magnetic field. A high-stability component of remanence is commonly observed in pseudo-single-domain grains. It has previously been assumed that the high stability must be due to SD-like regions in larger grains, but the micromagnetic simulations demonstrate that SD-like stability does not require a SD-like mechanism. ¿ 2000 American Geophysical Union