  We perform Monte Carlo simulations to study the two dimensional random-bond
XY model on a square lattice. Two kinds of bond randomness with the coupling
coefficient obeying the Gaussian or uniform distribution are discussed. It is
shown that the two kinds of disorder lead to similar thermodynamic behaviors if
their variances take the same value. This result implies that the variance can
be chosen as a characteristic parameter to evaluate the strength of the
randomness. In addition, the Berezinskii-Kosterlitz-Thouless transition
temperature decreases as the variance increases and the transition can even be
destroyed as long as the disorder is strong enough.
