A complexity classification of spin systems with an external field.
basic_science · Level V
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- Record sourced from PubMed, PMID 26443859.
- Also identified by DOI 10.1073/pnas.1505664112 and PMC identifier 4629322.
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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.