For stripes in doped antiferromagnets, we find that the ratio of spin and charge correlation lengths ${\ensuremath{\xi}}_{s}/{\ensuremath{\xi}}_{c}$ provides a sharp criterion for determining the dominant form of disorder in the system. If stripes are disordered predominantly by topological defects then ${\ensuremath{\xi}}_{s}/{\ensuremath{\xi}}_{c}\ensuremath{\lesssim}1.$ In contast, if stripes correlations are disordered primarily by nontopological elastic deformations (i.e., a Bragg-glass type of disorder) then $1<{\ensuremath{\xi}}_{s}/{\ensuremath{\xi}}_{c}\ensuremath{\lesssim}4$ is expected. Therefore, the observation of ${\ensuremath{\xi}}_{s}/{\ensuremath{\xi}}_{c}\ensuremath{\approx}4$ in $(\mathrm{LaNd}{)}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ and ${\ensuremath{\xi}}_{s}/{\ensuremath{\xi}}_{c}\ensuremath{\approx}3$ in ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{NiO}}_{4}$ invariably implies that the stripes are in a Bragg-glass-type state, and topological defects are much less relevant than commonly assumed. Expected spectral properties are discussed. Thus, we establish the basis for any theoretical analysis of the experimentally observed glassy state in these materials.
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