  Relying on the recently proposed multicanonical algorithm, we present a
numerical simulation of the first order phase transition in the 2d 10-state
Potts model on lattices up to sizes $100\times100$. It is demonstrated that the
new algorithm $lacks$ an exponentially fast increase of the tunneling time
between metastable states as a function of the linear size $L$ of the system.
Instead, the tunneling time diverges approximately proportional to $L^{2.65}$.
Thus the computational effort as counted per degree of freedom for generating
an independent configuration in the unstable region of the model rises
proportional to $V^{2.3}$, where $V$ is the volume of the system. On our
largest lattice we gain more than two orders of magnitude as compared to a
standard heat bath algorithm. As a first physical application we report a high
precision computation of the interfacial tension.
