9 problems

Ashkin–Teller magnetisation-field decomposition conjecture. The statement of the main magnetisation-field decomposition theorem holds for the Ashkin–Teller magnetisation field at e…

The Ashkin–Teller model on a box $\Lambda_n$ has configurations $(\sigma_1,\sigma_2):\Lambda_n\to\{-1,+1\}^2$ with density proportional to … On the self-dual line, assume $J\geq0$,…

Ashkin–Teller magnetisation-interface percolation conjecture. The law of the outermost interfaces of the Ashkin–Teller magnetisation field is the law of the outermost outer boundar…

Ashkin–Teller magnetisation exponent conjecture. The exponent of the magnetisation fields is constant and equal to

Monotonicity conjecture. For $\beta_1,\beta_2\in(0,1)$ with $\beta_1<\beta_2$, there exists $\varepsilon>0$ such that

Ashkin–Teller two-transition conjecture. In the ferromagnetic case, the Ashkin–Teller model on $\mathbb{Z}^2$ generally undergoes two phase transitions.

Kadanoff–Wegner–Wu–Lin conjecture. When $J<U$, the Ashkin–Teller model has two distinct transition lines: one governing correlations of the spins $\tau$ (or $\tau'$), and the other…

SLE conjecture. The curve $\gamma$ has the statistics of

SLE conjecture. The curve created by inserting parafermionic operators at two boundary points has the law