  We study the disorder-to-order transition in a collection of polar
self-propelled particles interacting through a distance dependent alignment
interaction. Strength of the interaction, $a^{d}$ ($0<a<1$) decays with metric
distance $d$ between particle pair, and the interaction is short range. At $a =
1.0$, our model reduces to the famous Vicsek model. For all ${\it a}>0$, the
system shows a transition from a disordered to an ordered state as a function
of noise strength. We calculate the critical noise strength, $\eta_c(a)$ for
different $a$ and compare it with the mean-field result. Nature of the
disorder-to-order transition continuously changes from discontinuous to
continuous with decreasing $a$. We numerically estimate tri-critical point
$a_{TCP}$ at which the nature of transition changes from discontinuous to
continuous. The density phase separation is large for ${\it a}$ close to unity,
and it decays with decreasing $a$. We also write the coarse-grained
hydrodynamic equations of motion for general ${\it a}$, and find that the
homogeneous ordered state is unstable to small perturbation as ${\it a}$
approaches to $1$. The instability in the homogeneous ordered state is
consistent with the large density phase separation for ${\it a}$ close to
unity.
