Abstract
We take the first step toward a classification of the approximation complexity of the six-vertex model. This is a subject of extensive research in statistical physics. Our result concerns the approximability of the partition function on 4-regular graphs, classified according to the parameters of the model. Our complexity results conform to the phase transition phenomenon from physics. We show that the approximation complexity of the six-vertex model behaves dramatically differently on the two sides separated by the phase transition threshold. Furthermore, we present structural properties of the six-vertex model on planar graphs for parameter settings that have known relations to the Tutte polynomial T(G; x, y).
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