We consider the one-dimensional ferromagnetical Ising model with long-range interaction under external field blocks of equal length with alternating signs and investigate the low-temperature phase diagram of this model. It turns out that when the absolute value of the external field is sufficiently small, the set of Gibbs states substantially depends on block size: at small block sizes there are at least two Gibbs states and at large block sizes there is a unique Gibbs state. © 2007 IOP Publishing Ltd.