11 problems

Consider the $(7,5,-1)$ model, whose low-lying excitation data are consistent with those of the $(7,3,-1)$ model. The relevant sector is a conformal field theory with central charg…

The $(5,3,+1)$ model is a critical clock model or anyon chain whose low-energy spectrum is described by a conformal field theory. Based on the observed spectrum, the Ising-product…

Fix $q\geq 5$. Consider the nearest-neighbor $q$-state clock model and the three temperature regimes: a low-temperature regime, an intermediate regime, and a high-temperature regim…

Let $\beta$ be the inverse temperature, let $\beta_c$ denote the critical inverse-temperature threshold, and let $q$ be the number of clock states. The notation $O(q^2)$ denotes th…

Consider the nearest-neighbor $q$-state clock model in spatial dimension $d\geq 3$, at inverse temperature below the critical-temperature threshold and with $q$ sufficiently large.…

Rotating-state structure conjecture. In the regime $\beta_N^{cr}<\beta<\beta_N^G$ and $d>0$, there is a unique translation-invariant stationary distribution…

Continuum rotating-states conjecture. For every sufficiently large $\beta$, there exists $N=N(\beta)$ such that, for every $N\geq N(\beta)$ and every $d>0$, the driven $N$-clock mo…

Vanishing critical-drift conjecture. The critical drift is positive at low temperatures and satisfies

Rotating-state conjecture. For every $N\geq\bar N$ and $\beta>\beta_N^{cr}$, there exists a critical drift $d_{cr}(\beta,N)>0$ such that, if $|d|<d_{cr}(\beta,N)$, then…

Fix $q\geq 5$ and consider the temperature regimes of the nearest-neighbor clock model: a low-temperature regime, an intermediate regime, and a high-temperature regime. Let the two…

Consider the nearest-neighbor clock model in a higher-dimensional bipartite lattice, with spins taking $q$ discrete values and an intermediate-temperature phase between the low-tem…