Bloch-wall phase transition in the spherical model

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets is investigated for the model of D-component classical spin vectors in the limit D --> infinity. This exactly solvable model is equivalent to the standard spherical model in the homogeneous case, but deviates from it and is free from unphysical behaviour in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch-wall order parameter) result in the diminishing of the wall transition temperature T-B in comparison to its mean-field value, thus favouring the existence of linear walls. For finite values of T-B an additional anisotropy in the basis plane x, y is required; in purely uniaxial ferromagnets a domain wall behaves like a two-dimensional system with a continuous spin symmetry and does not order into the Bloch one.