Abstract
A time-dependent Ising model within the Bethe-Peierls approximation is examined in light of the recent work by Eggarter which stresses the importance of boundary terms in the treatment of the phase transition. In particular, an equation for the order parameter is obtained from Glauber's master equation, and this agrees with the result of Huang; however, the use of a usual self-consistency condition (violated on the boundary) is avoided. The time-dependent equation is of the form of those used recently within the mean-field approximation for weak external fields.
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