  The concept of replica symmetry breaking found in the solution of the
mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a
variety of problems in science ranging from biological to computational and
even financial analysis. Thus it is of paramount importance to understand which
predictions of the mean-field solution apply to non-mean-field systems, such as
realistic short-range spin-glass models. The one-dimensional spin glass with
random power-law interactions promises to be an ideal test-bed to answer this
question: Not only can large system sizes-which are usually a shortcoming in
simulations of high-dimensional short-range system-be studied, by tuning the
power-law exponent of the interactions the universality class of the model can
be continuously tuned from the mean-field to the short-range universality
class. We present details of the model, as well as recent applications to some
questions of the physics of spin glasses. First, we study the existence of a
spin-glass state in an external field. In addition, we discuss the existence of
ultrametricity in short-range spin glasses. Finally, because the range of
interactions can be changed, the model is a formidable test-bed for
optimization algorithms.
