abstract: The quantum Ising model with transverse field on the $d$-dimensional cubic lattice belongs to those quantum statistical machanical models which can be described in terms of interacting two sided markov processes. In turn, these systems admit a description in terms of suitable Gibbs random fields, in the case at hand on a $d+1$-dimensional lattice. In this talk we will introduce the model and its representations and discuss some results about the entanglement properties of the ground state of the model as well as the decay of correlations.