Monodromy fields on I3 are a family of lattice fields in two dimensions which are a natural generalisation of the two dimensional Ising field occurring in the C*-algebra approach to Statistical Mechanics. A criterion for the critical limit one point correlation of the monodromy field tra(M) at a 6 l3, Um(#.(M)). is deduced for matrices M € GL(p, C) having non-negative eigenvalues. Using this criterion a non-identity 2x2 matrix is found with a finite critical limit one point correlation. The general set of p x p matrices with finite critical limit one point correlations is also considered and a conjecture for the critical limit n point correlations postulated. The boson-fermion correspondence for the representation of the CAR algebra over L3(Sl, C) defined by the (t,B) KMS state with chemical potential p is considered and the non-bijectivity shown. Using an alternative formulation the correlations are recalculated leading to a determinant identity reminiscent of Saego’s Theorem.