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For the spin-glass chain in an external field $h$, a non-zero weight at theorigin of the bond distribution $\rho (J)$ is known to induce a non-analyticalmagnetization at zero temperature : for $\rho(J) \sim A | J |^{\mu-1}$ near $J\to 0$, the magnetization follows the Chen-Ma scaling $M \sim h^{\mu/(2+\mu)}$.In this paper, we numerically revisit this model to obtain detailed statisticalinformation on the ground state configuration and on the low-energy two-levelexcitations that govern the low temperature properties. The ground stateconsists of long unfrustrated intervals separated by weak frustrated bonds: Weaccordingly compute the strength distribution of these frustrated bonds, aswell as the length- and magnetization- distributions of the unfrustratedintervals. We find that the low-energy excitations are of two types (i) onefrustrated bond of the ground state may have two positions that are nearlydegenerate in energy (ii) two neighboring frustrated bonds of the ground statemay be annihilated or created with nearly zero energy cost. For each excitationtype, we compute its probability density as a function of its length. Wemoreover show that the contributions of these excitations to variousobservables (specific heat, Edwards-Anderson order parameter, susceptibility)are in full agreement with direct transfer matrix evaluations at lowtemperature. Finally, following the special bimodal case $\pm J$, where aMa-Dasgupta RG procedure has been previously used to compute explicitly theabove observables, we discuss the possibility of an extended RG procedure : wefind that the ground state can be seen as the result of a hierarchical`fragmentation' procedure that we describe.Comment: 15 pages, 8 figure

Spin-glass chain in a magnetic field: Influence of the disorder distribution on ground-state properties and low-energy excitations