  Extensive Monte Carlo study of two-dimensional Ising model is done to
investigate the statistical behavior of spin clusters and interfaces as a
function of temperature, $T$. We use a \emph{tie-breaking} rule to define
interfaces of spin clusters on square lattice with strip geometry and show that
such definition is consistent with conformal invariant properties of interfaces
at critical temperature, $T_c$. The \emph{effective} fractal dimensions of spin
clusters and interfaces ($d_c$ and $d_I$, respectively) are obtained as a
function of temperature. We find that the effective fractal dimension of the
spin clusters behaves almost linearly with temperature in three different
regimes. It is also found that the effective fractal dimension of the
interfaces undergoes a sharp crossover around $T_c$, between values 1 and 1.75
at low and high temperatures, respectively. We also check the finite-size
scaling hypothesis for the percolation probability and the average mass of the
largest spin-cluster in a good agreement with the theoretical predictions.
