A partially annealed mean-field spin-glass model with a locally embedded
pattern is studied. The model consists of two dynamical variables, spins and
interactions, that are in contact with thermal baths at temperatures T_S and
T_J, respectively. Unlike the quenched system, characteristic correlations
among the interactions are induced by the partial annealing. The model exhibits
three phases, which are paramagnetic, ferromagnetic and spin-glass phases. In
the ferromagnetic phase, the embedded pattern is stably realized. The phase
diagram depends significantly on the ratio of two temperatures n=T_J/T_S. In
particular, a reentrant transition from the embedded ferromagnetic to the
spin-glass phases with T_S decreasing is found only below at a certain value of
n. This indicates that above the critical value n_c the embedded pattern is
supported by local field from a non-embedded region. Some equilibrium
properties of the interactions in the partial annealing are also discussed in
terms of frustration.Comment: 8pages, 4figure
