  The fractal dimensions and the percolation exponents of the geometrical spin
clusters of like sign at criticality, are obtained numerically for an Ising
model with temperature-dependent annealed bond dilution, also known as the
thermalized bond Ising model (TBIM), in two dimensions. For this purpose, a
modified Wolff single-cluster Monte Carlo simulation is used to generate
equilibrium spin configurations on square lattices in the critical region. A
tie-breaking rule is employed to identify non-intersecting spin cluster
boundaries along the edges of the dual lattice. The values obtained for the
fractal dimensions of the spanning geometrical clusters $D_{c}$, and their
interfaces $D_{I}$, are in perfect agreement with those reported for the
standard two-dimensional ferromagnetic Ising model. Furthermore, the variance
of the winding angles, results in a diffusivity $\kappa=3$ for the
two-dimensional thermalized bond Ising model, thus placing it in the
universality class of the regular Ising model. A finite-size scaling analysis
of the largest geometrical clusters, results in a reliable estimation of the
critical percolation exponents for the geometrical clusters in the limit of an
infinite lattice size. The percolation exponents thus obtained, are also found
to be consistent with those reported for the regular Ising model. These
consistencies are explained in terms of the Fisher renormalization relations,
which express the thermodynamic critical exponents of systems with annealed
bond dilution in terms of those of the regular model system.
