Exact solution of the Glauber-Ising model on the finite-length semi-open chain (opens in new tab)

The exact time-space correlation function of the $1D$ Glauber-Ising model, quenched to temperature $T=0$ and on a semi-open lattice of finite size $N$, is obtained. This also allows to deduce the exact empty-interval probability of the dual $1D$ coagulation-diffusion process on a periodic finite ring and to reproduce the long-time decay of the particle concentration. These results are consistent with the generic expectations of dynamical finite-...