  We obtain asymptotic expansions for Toeplitz determinants corresponding to a
family of symbols depending on a parameter $t$. For $t$ positive, the symbols
are regular so that the determinants obey Szeg\H{o}'s strong limit theorem. If
$t=0$, the symbol possesses a Fisher-Hartwig singularity. Letting $t\to 0$ we
analyze the emergence of a Fisher-Hartwig singularity and a transition between
the two different types of asymptotic behavior for Toeplitz determinants. This
transition is described by a special Painlev\'e V transcendent. A particular
case of our result complements the classical description of Wu, McCoy, Tracy,
and Barouch of the behavior of a 2-spin correlation function for a large
distance between spins in the two-dimensional Ising model as the phase
transition occurs.
