  The effect of inclusion of higher-order interactions in the {\it XY} model on
critical properties is studied by Monte Carlo simulations. It is found that an
increasing number of the higher-order terms in the Hamiltonian modifies the
shape of the potential, which beyond a certain value leads to the change of the
nature of the transition from continuous to first order. The evidence for the
first-order transition is provided in the form of the finite-size scaling and
the energy histogram analysis. A rough phase diagram is presented as a function
of the number of the higher-order interaction terms.

Statistical Mechanics