arXiv subjects
Publications and source records attributed to Vincent Pasquier.
We construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke algebras. The center of the affine Hecke algebras coincides with commuting Hamiltonians. These Hamiltonians have q-deformed affine Lie algebras as symmetry algebra.
In the zero temperature Glauber dynamics of the ferromagnetic Ising or $q$-state Potts model, the size of domains is known to grow like $t^{1/2}$. Recent simulations have shown that the fraction $r(q,t)$ of spins which have never flipped up to time $t$ decays like a power law $r(q,t) \sim t^{-θ(q)}$ with a non-trivial dependence of the exponent $θ(q)$ on $q$ and on space dimension. By mapping the problem on an exactly soluble one-species coagulation model ($A+A\rightarrow A$), we obtain the exact expression of $θ(q)$ in dimension one.