Invariant Subspaces of the Stochastic Ising High Temperature Dynamics
1996, v.2, Issue 2, 263-284
We consider a stochastic Ising model (Glauber dynamics) for high values of the temperature. It is shown that there are several invariant subspaces with respect to the generator $L$ of the dynamics and with respect to the group of translations (one-, two-, ..., $k$-particle subspaces). The spectra of $L$ in these subspaces do not overlap. The spectrum of $L$ in the first (one-particle) subspace is studied in more detail. Using these results, we find the asymptotics of the decay of the correlations of the random field.
Keywords: Glauber dynamics,generator,spectra of linear operators,invariant subspaces,decay of correlations