  We consider quasistatic fiber bundle models with interactions. Classical load
sharing rules are considered, i.e. local, global or decaying as a power-law of
distance. All fibers are identically elastic, initially intact, and break at a
random threshold picked from a quenched disorder (q.d.) distribution. We are
interested in the probability distribution of configurations of broken fibers
at a given elongation, averaged over all possible realizations of the
underlying q.d.. This distribution is accessed by mapping the threshold set
space onto the configurational space, each path corresponding to the evolution
of a bundle corresponding to a realized q.d.. Using a perturbative approach
allows to obtain this distribution to leading order in the interactions. This
maps this system onto classical statistical mechanics models, i.e. percolation,
standard or generalized Ising models depending on the range of the interactions
chosen in the load sharing rule. This relates such q.d. based systems to
standard classical mechanics, which allows to derive observables of the system,
as e.g. correlation lengths. The thermodynamic parameters formally equivalent
to temperature and chemical potential, are functions of the externally imposed
deformation, depending on the load sharing rule and the choice of the q.d.
distribution.
