Random Walk Analysis of the Commensurate-Incommensurate Transition in the Isotropic Spin-1 Chain


It has been observed that in the isotropic spin-1 chain a transition in the asymptotic properties of the correlation function (commensurate-incommensurate transition) occurs at the AKLT point. We propose a simple random-walk-type argument, explaining this transition. Also, we consider a modification of the AKLT model, for which this argument can be turned into a rigorous proof.

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Yarotsky, D.A. Random Walk Analysis of the Commensurate-Incommensurate Transition in the Isotropic Spin-1 Chain. J Stat Phys 130, 957–981 (2008). https://doi.org/10.1007/s10955-007-9458-y

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  • Commensurate-incommensurate transition
  • Isotropic spin-1 chain
  • AKLT model