The Ashkin-Teller model is a lattice spin model coupling two Ising spins
at each vertex through both pair interactions and a four-spin interaction across
each edge. In the symmetric zero-field convention the configuration weight is proportional
to
At
the two Ising systems are independent. For suitable planar parameters, a current
representation also couples primal and dual cluster collections with a height function.
The two currents are generally not complementary, since both members of a mutually
dual edge pair may be closed.
Alcalde López, T.; Heeney, L.; and Lis, M. "The Ising Magnetisation Field and the Gaussian Free Field." 5 Feb 2026. https://arxiv.org/abs/2602.05886.Lis,
M. "Spins, Percolation and Height Functions." Electron. J. Probab.27,
Article 35, 1-21, 2022. https://doi.org/10.1214/22-EJP761.
at each vertex through both pair interactions and a four-spin interaction across
each edge. In the symmetric zero-field convention the configuration weight is proportional
to
![expsum_(ij in E)[J(sigma_isigma_j+tau_itau_j)+Usigma_isigma_jtau_itau_j].](/images/equations/Ashkin-TellerModel/NumberedEquation1.svg)
the two Ising systems are independent. For suitable planar parameters, a current
representation also couples primal and dual cluster collections with a height function.
The two currents are generally not complementary, since both members of a mutually
dual edge pair may be closed.
