Approximability of the Six-vertex Model

Jin-Yi Cai; Tianyu Liu; Pinyan Lu

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arXiv · 1712.05880

Approximability of the Six-vertex Model

Jin-Yi Cai·Tianyu Liu·Pinyan Lu

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Abstract

In this paper we take the first step toward a classification of the approximation complexity of the six-vertex model, an object of extensive research in statistical physics. 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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Jin-Yi Cai, Tianyu Liu, Pinyan Lu. 2017-12-16. Approximability of the Six-vertex Model. https://arxiv.org/abs/1712.05880

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