  Unlike conformal boundary conditions, conformal defects of Virasoro minimal
models lack classification. Alternatively to the defect perturbation theory and
the truncated conformal space approach, we employ open string field theory
(OSFT) techniques to explore the space of conformal defects. We illustrate the
method by an analysis of OSFT around the background associated to the $(1,2)$
topological defect in diagonal unitary minimal models. Numerical analysis of
OSFT equations of motion leads to an identification of a nice family of
solutions, recovering the picture of infrared fixed points due to Kormos,
Runkel and Watts. In particular, we find a continuum of solutions in the Ising
model case and 6 solutions for other minimal models. OSFT provides us with
numerical estimates of the g-function and other coefficients of the boundary
state.
