A complexity classification of spin systems with an external field.

Goldberg, Leslie Ann; Jerrum, Mark · Proc Natl Acad Sci U S A · 2015

basic_science · Level V

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Abstract

We study the computational complexity of approximating the partition function of a q-state spin system with an external field. There are just three possible levels of computational difficulty, depending on the interaction strengths between adjacent spins: (i) efficiently exactly computable, (ii) equivalent to the ferromagnetic Ising model, and (iii) equivalent to the antiferromagnetic Ising model. Thus, every nontrivial q-state spin system, irrespective of the number q of spins, is computationally equivalent to one of two fundamental two-state spin systems.