An Ising model in a magnetic field with a boundary

We obtain the diagonal reflection matrices for a recently introduced family of dilute A_L lattice models in which the A₃ model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from the crossing-unitarity relation and thus directly obtain the critical magnetic surface exponent δ_s for L odd and surface specific heat exponent for L even in each of the various regimes. For L = 3 in the appropriate regime we obtain the Ising exponent δ_s = -15/7, which is the first determination of this exponent without the use of scaling relations.