An Ising model in a magnetic field with a boundary

Abstract

We obtain the diagonal reflection matrices for a recently introduced family of dilute ${\mathrm{A}}_L$ lattice models in which the ${\mathrm{A}}_3$ 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 ${\delta }_s$ 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 ${\delta }_s=-\frac{15}{7}$, which is the first determination of this exponent without the use of scaling relations.

7 pages, LaTeX