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We study the 1D quantum Heisenberg chain with randomly ferromagnetic orantiferromagnetic couplings (a model previously studied by approximatestrong-disorder renormalization group). We find that, at least for sufficientlylarge spin $S$, the ground state has "spin glass" order. The spin waves on topof this state have the dynamical exponent ${z=3/2}$, intermediate between thevalues $z=1$ of the antiferromagnet and ${z=2}$ of the ferromagnet. DMRGsimulations 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 suggestthat this case is also ordered, but with a small ordered moment.

Heisenberg spin chain with random-sign couplings