Loss without recovery of gibbsianness during diffusion of continuous spins (Q2494408)

The time evolution of a continuous-spin initial measure which is a Gibbs measure for a Hamiltonian with quadratic nearest neighbor interaction and a priori single-site double-well potential that has a special form is studied. For ``high temperature'' initial measures it is proven that the time-evolved measure \(\mu_t\) is Gibbsian for all \(t.\) For ``low temperature'' initial measures it is proven that \(\mu_t\) stays Gibbsian for small enough times \(t,\) but loses its Gibbsian character for large enough \(t.\)