On the location of the 1-particle branch of the spectrum of the disordered stochastic Ising model

Abstract

We analyse the lower non trivial part of the spectrum of the generator of theGlauber dynamics for a $d$-dimensional nearest neighbour Ising model with abounded random potential. We prove conjecture 1 in [1]: forsufficiently large values of the temperature, the first band of the spectrum ofthe generator of the process coincides with a closed non random segment of thereal line.