  Let $\Sigma_{A}$ be a topologically mixing shift of finite type, let
$\sigma:\Sigma_{A}\to\Sigma_{A}$ be the usual left-shift, and let $\mu$ be the
Gibbs measure for a H\"{o}lder continuous potential that is not cohomologous to
a constant. In this paper we study recurrence rates for the dynamical system
$(\Sigma_{A},\sigma)$ that hold $\mu$-almost surely. In particular, given a
function $\psi:\mathbb{N}\to \mathbb{N}$ we are interested in the following set
$$R_{\psi}=\{{\texttt i}\in \Sigma_{A}:i_{n+1}\ldots i_{n+\psi(n)+1}=i_1\ldots
i_{\psi(n)}\textrm{ for infinitely many }n\in\mathbb{N}\}.$$
  We provide sufficient conditions for $\mu(R_{\psi})=1$ and sufficient
conditions for $\mu(R_{\psi})=0$. As a corollary of these results, we discover
a new critical threshold where the measure of $R_{\psi}$ transitions from zero
to one. This threshold was previously unknown even in the special case of a
non-uniform Bernoulli measure defined on the full shift. The proofs of our
results combine ideas from Probability Theory and Thermodynamic Formalism. In
our final section we apply our results to the study of dynamics on self-similar
sets.
