Static properties of Potts spin chains

One-dimensional a-state Potts spin glasses (SG) disordered ferromagnets (DFM) and +/- J systems are studied. The energy minima (EM) and magnetization with their distributions are exactly calculated. The stable local EM of no more than 27-spin chains with periodic boundary conditions are analyzed. All these systems have an exponentially growing numbers of average energy minima Versus number of spins. The frustration effect is also discussed for some particular samples. The investigation of metastable states shows that the energy minima distributions for all our systems approach the normal distribution. The SG and DFM have identical distributions of energy minima. The systems studied here differ merely by the properties of the magnetization. The absolute value of magnetization averaged over all the EM decreases logarithmically with the number of spins for the three systems.