  We study the critical line of the triangular Ising antiferromagnet in an
external magnetic field by means of a finite-size analysis of results obtained
by transfer-matrix and Monte Carlo techniques. We compare the shape of the
critical line with predictions of two different theoretical scenarios. Both
scenarios, while plausible, involve assumptions. The first scenario is based on
the generalization of the model to a vertex model, and the assumption that the
exact analytic form of the critical manifold of this vertex model is determined
by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights.
However, it is not possible to fit the coefficients of such polynomials of
orders up to 10, such as to reproduce the numerical data for the critical
points. The second theoretical prediction is based on the assumption that a
renormalization mapping exists of the Ising model on the Coulomb gas, and
analysis of the resulting renormalization equations. It leads to a shape of the
critical line that is inconsistent with the first prediction, but consistent
with the numerical data.
