Convergence Properties of Quasi-Particles of Various Species in the Stochastic Blume-Capel Model

#### E. Zhizhina

2004, v.10, №2, 307-326

ABSTRACT

We construct two leading invariant subspaces of the generator of the stochastic Blume - Capel model under high temperatures, describing states of two various quasi-particles. We show that the corresponding spectrum branches of the generator occupy small vicinities of the point $-1$ and prove that the restrictions of the generator to these invariant subspaces have different spectral gaps.

Keywords: Glauber dynamics,invariant subspaces of thegenerator,spectral gap