Nonexistence of metastable states in a one-dimensional Heisenberg model spin-glass

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Abstract
It is shown that in the classical Heisenberg linear chain with arbitrary nearest-neighbor interactions and nonzero but otherwise arbitrary next-nearest-neighbor interactions there are no metastable states. Since these models include examples with random and strongly competing exchange interactions (i.e., model spin-glasses), this result tends to run counter to the rather widely held notion that such competition aided by randomness causes the existence of a large number of low-energy local minima. In addition, some explicit metastable states are exhibited for a nonrandom planar spin model, and remarks on previous work are given which show that the question of the existence of a large number of low-lying local minima in two- and three-dimensional vector-spin model spin-glasses remains unanswered.

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