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At T = 0 and a sufficiently large field, the nearest-neighborantiferromagnetic Ising chain undergoes a first-order spin-flop transition intothe ferromagnetic phase. We consider its smearing under the random-bonddisorder such that all independent random bonds are antiferromagnetic (AF). Itis shown that it can be described exactly for arbitrary distribution of AFbonds P(J). Moreover, the site magnetizations of finite chains can be foundanalytically in this model. We consider continuous P(J) which is zero abovesome -J_1 and behaves near it as (-J_1 - J)^\lambda, \lambda > -1. In this caseferromagnetic phase emerges continuously in a field H > H_c = 2J_1. At 0 >\lambda > -1 it has usual second-order anomalies near H_c with critical indicesobeying the scaling relation and depending on \lambda . At \lambda > 0 thehigher-order transitions appear (third, fourth etc.) marked by the divergenceof corresponding nonlinear susceptibilities. In the chains with even number ofspins the intermediate "bow-tie" phase with linearly modulated AF order existsbetween AF and ferromagnetic ones at J_1 < H < H_c. Its origin can be traced tothe infinite correlation length of the degenerate AF phase from which itemerges. This implies the existence of similar inhomogeneous phases with size-and form-dependent order in a number of other systems with infinite correlationlength. The possibility to observe the signs of "bow-tie" phase in low-Tneutron diffraction experiments is discussed.

Smeared spin-flop transition in random antiferromagnetic Ising chain