Approximability of the Eight-vertex Model

Understand

We initiate a study of the classification of approximation complexity of the eight-vertex model defined over 4-regular graphs.

• The eight-vertex model, together with its special case the six-vertex model, is one of the most extensively studied models in statistical physics, and can be stated as a problem of counting weighted orientations in graph theory.
• Our result concerns the approximability of the partition function on all 4-regular graphs, classified according to the parameters of the model.
• Our complexity results conform to the phase transition phenomenon from physics.