Gradient fields of low-temperature spin models (Ising, Potts, beach, six-vertex) are finitary factors of i.i.d. processes even when the models themselves are not.
Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
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abstract
The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective is then employed in the proof that the Pfaffian structure of boundary correlations emerges asymptotically at criticality in Ising models on $\mathbb Z^2$ with finite-range interactions. The analysis is enabled by new results on the stochastic geometry of the corresponding random currents. The proven statement establishes an aspect of universality, seen here in the emergence of fermionic structures in two dimensions beyond the solvable cases.
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Finitary codings for gradient models and a new graphical representation for the six-vertex model
Gradient fields of low-temperature spin models (Ising, Potts, beach, six-vertex) are finitary factors of i.i.d. processes even when the models themselves are not.