Results sufficient conditions for FPTAS for classes of spin systems general multi-spin system: Ae(x,y) in terms of c= max e∈D Ae(w,2) w,x,y,z∈[q ●( Gamarnik-Katz'07:(cA-c-a)△g△<1 this paper::3△(cA-1)≤1 an exponential improvement! on Potts model (with inverse temperature B): it implies:3△(ell-1)≤1Results • general multi-spin system: • Gamarnik-Katz’07: • on Potts model (with inverse temperature β): sufficient conditions for FPTAS for classes of spin systems (c￾ ￾ c￾￾)￾q￾ < 1 in terms of it implies: 3￾(e|￾| ￾ 1)  1 c = max e2E w,x,y,z2[q] Ae(x, y) Ae(w, z) this paper: 3￾(c￾ ￾ 1)  1 an exponential improvement!