Peierles transition in a linear chain of exchange related spins

The loss of stability of the antiferromagnetic state of matter respective to the Peierls transition is calculated in the framework of a new model of magnetic sublattices. In this new model, in contrast to the Anderson-Ziman sublattice model, the antiferromagnetic spin ordering is provided by a weak influence of magnetic anisotropy. Magnetic anisotropy suppresses exchange mixing with a sufficiently large number of spins in the sublattice . The Peierls transition consists in the deformation in a linear chain of atoms, namely the convergence of neighboring atoms, at which the period of the crystal lattice increases by factor of two. When atoms approach, exchange interaction is established between a pair of nearest atomic spins only. Based on the new model of magnetic sublattices, the antiferromagnetic sublattice state of the periodic chain of spins is found to be unstable respective to the transition to the Peierls state. During the transition to the "spin-Peierls" state, the spins of neighboring atoms will be ordered antiparallelly, but since there is no preferred direction of spin ordering, it is impossible to introduce the concept of magnetic sublattices. Such magnetic states can be suggested from the exponential dependence of the magnetic susceptibility on the reciprocal temperature. The electrons magnetism in this state is determined by the atomic diamagnetism if the frequencies of thermal motion are small compared to the exchange frequency.