ON THE LOCATION OF THE 1-PARTICLE BRANCH OF THE SPECTRUM OF THE DISORDERED STOCHASTIC ISING MODEL

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