5 problems

Two-transition conjecture. There exists $\bar N$ such that, for every $N\geq\bar N$, the model undergoes two phase transitions: for

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.…

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…

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…