Summary
It is shown that a spin system on ℤ has only one invariant probability measure if it has attractive or repulsive nearest neighbor flip rates which are strictly positive and periodic under translation along ℤ.
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Research supported in part by NSF Grant MCS 78-01168 A04
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Gray, L.F. The positive rates problem for attractive nearest neighbor spin systems on ℤ. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 389–404 (1982). https://doi.org/10.1007/BF00539839
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DOI: https://doi.org/10.1007/BF00539839