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Physical review. B, Solid state

q -dependent magnetic susceptibility of a disordered linear chain

George Theodorou, Morrel H. Cohen

Published Nov 1, 1977• 3 citations
Publisher

Abstract

The $q$-dependent magnetic susceptibility for disordered Ising and classical Heisenberg chains is calculated. The coupling between spins is of the form $J(n)={J}_{0}{e}^{\ensuremath{-}\ensuremath{\beta}(n\ensuremath{-}1)}$, $\ensuremath{\beta}>0$, with $n$ the random number of interatomic units between neighboring spins. The cases where $J$ is ferromagnetic or antiferromagnetic or of spin-glass type are examined.

DOI
10.1103/physrevb.16.3955

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We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings [a model previously studied by approximate strong-disorder renormalization group (RG)]. We find that, at least for sufficiently large spin S , the ground state has “spin glass” order. The spin waves on top of this state have the dynamical exponent z = 3 / 2 , intermediate between the values z = 1 of the antiferromagnet and z = 2 of the ferromagnet. Density matrix renormalization group (DMRG) simulations are in good agreement with the analytical results for spins S = 1 and S = 3 / 2 . The case S = 1 / 2 shows large finite size effects: We suggest that this case is also ordered, but with a small ordered moment.
We study the magnetic properties of two types of one-dimensional XXXXXX spin-12\frac{1}{2}21​ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.
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