romagnet ic ▁Is ing ▁model ▁below ▁the ▁critical ▁temperature , ▁there ▁are ▁two ▁pure ▁states , ▁the ▁" most ly - up " ▁and ▁" most ly - down " ▁states , ▁which ▁are ▁inter changed ▁under ▁the ▁model ' s ▁ ▁symmetry . ▁ ▁Mark ov ▁property ▁An ▁example ▁of ▁the ▁Mark ov ▁property ▁can ▁be ▁seen ▁in ▁the ▁Gib bs ▁measure ▁of ▁the ▁Is ing ▁model . ▁The ▁probability ▁for ▁a ▁given ▁spin ▁ ▁to ▁be ▁in ▁state ▁s ▁could , ▁in ▁principle , ▁depend ▁on ▁the ▁states ▁of ▁all ▁other ▁sp ins ▁in ▁the ▁system . ▁Thus , ▁we ▁may ▁write ▁the ▁probability ▁as ▁ ▁. ▁ ▁However , ▁in ▁an ▁Is ing ▁model ▁with ▁only ▁finite - range ▁interactions ▁( for ▁example , ▁nearest - ne igh bor ▁interactions ), ▁we ▁actually ▁have ▁ ▁, ▁ ▁where ▁ ▁is ▁a ▁neighborhood ▁of ▁the ▁site ▁. ▁That ▁is , ▁the ▁probability ▁at ▁site ▁ ▁depends ▁only ▁on ▁the ▁sp ins ▁in ▁a ▁finite ▁neighborhood . ▁This ▁last ▁equation ▁is ▁in ▁the ▁form ▁of ▁a ▁local ▁Mark ov ▁property . ▁Me asures ▁with ▁this ▁property ▁are ▁sometimes ▁called ▁Mark ov ▁random ▁fields . ▁ ▁More ▁strongly , ▁the ▁con verse ▁is ▁also ▁true : ▁any ▁positive ▁probability ▁distribution ▁( non zero ▁density ▁everywhere ) ▁having ▁the ▁Mark ov ▁property ▁can ▁be ▁represented ▁as ▁a ▁Gib bs ▁measure ▁for ▁an ▁appropriate ▁energy ▁function . ▁This ▁is ▁the ▁Hamm ers ley – Cl iff ord ▁theorem . ▁ ▁F ormal ▁definition ▁on ▁l