Smeared spin-flop transition in random antiferromagnetic Ising chain

TL;DR

This paper analyzes how random-bond disorder smears the spin-flop transition in a 1D antiferromagnetic Ising chain, revealing exact solutions, phase emergence, and critical behaviors, including a novel intermediate 'bow-tie' phase.

Contribution

It provides an exact analytical description of the smeared spin-flop transition under disorder and uncovers the existence of an inhomogeneous 'bow-tie' phase in finite chains.

Findings

Exact solution for magnetization in disordered chains.

Emergence of a continuous ferromagnetic phase at H > H_c.

Identification of a 'bow-tie' inhomogeneous phase with modulated AF order.

Abstract

At T = 0 and a sufficiently large field, the nearest-neighbor antiferromagnetic Ising chain undergoes a first-order spin-flop transition into the ferromagnetic phase. We consider its smearing under the random-bond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that it can be described exactly for arbitrary distribution of AF bonds P(J). Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider continuous P(J) which is zero above some -J_1 and behaves near it as (-J_1 - J)^\lambda, \lambda > -1. In this case ferromagnetic 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 indices obeying the scaling relation and depending on \lambda . At \lambda > 0 the higher-order transitions appear (third, fourth etc.) marked by the divergence of corresponding nonlinear susceptibilities. In the chains with even number of spins the intermediate "bow-tie" phase with linearly modulated AF order exists between AF and ferromagnetic ones at J_1 < H < H_c. Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size- and form-dependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of "bow-tie" phase in low-T neutron diffraction experiments is discussed.