Theory of the anticontinuous limit for spin Hamiltonians. Search for discrete breather modes

We generalize the theory of extending breather solutions in the anticontinuous limit to the case of discrete spin systems. We formulate necessary conditions and determine the upper bound for the intersite coupling constant for which the extension procedure is possible. Using a numerical algorithm, we obtain breather modes of a discrete spin chain related to single-site and two-site excitations of the anticontinuous limit and show their linear stability.