The problem of formation of incipient magnetic domain in the scheme of Brown's equation is one of the typical problems of bifurcation. A scale transformation is introduced, so that the size of a ferromagnetic body appears explicitly as a parameter in the expressions of free energy and Brown's equation. We generalize the perturbation method in bifurcation theory to study the initial bifurcation of Brown's equation. After an analysis of the stability of single-domain state and bifurcation solutions, we arrived at the conclusion that the critical size of incipient domain formation equals to the smallest positive bifurcation point of size parameter and the process of incipient domain formation takes place either continuously following the bifurcation solutions starting from this bifurcation point or discontinuously with a jump at this point. The criteria for discriminating the continuity and discontinuity of such a transition were given. In addition, we also obtained the lower and upper limits of the precise critical size of single-domain, and also its exact value in particular cases.
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