Spin System undirected graph G=(V,E) finite integer g≥2 configuration o∈[gl' weight:w(o)=A(ou,)b(o) {u,w}∈E u∈V A:[ql×[q→R≥o symmetric gxg matrix (symmetric binary constraint) b:[q→R>0 g-vector (unary constraint) partition function: Zc=∑w(a) o∈[gV Gibbs distribution: c(o)= w(o) ZGSpin System undirected graph G = (V, E) finite integer q ≥ 2 ￾ 2 [q] V configuration w(￾) = Y {u,v}2E A(￾u, ￾v) Y v2V weight: b(￾v) A : [q] ⇥ [q] ! R￾0 b : [q] ! R￾0 symmetric q×q matrix q-vector (symmetric binary constraint) partition function: ZG = X ￾2[q]V w(￾) Gibbs distribution: µG(￾) = w(￾) ZG (unary constraint)