The paper presents a numerical simulation of the first-order phase transition in the 2D 10-state Potts model using the multicanonical Monte Carlo (MC) algorithm. The authors demonstrate that the multicanonical algorithm significantly reduces the computational effort compared to standard heat bath algorithms, especially for large lattice sizes. The tunneling time between metastable states diverges approximately as \( L^{2.65} \), where \( L \) is the linear size of the system, leading to a computational cost of \( V^{2.3} \) per degree of freedom. This improvement is crucial for studying first-order phase transitions, where critical slowing down is a significant issue. The paper also reports a high-precision computation of the interfacial free energy, which is a key quantity in understanding the interface between disordered and ordered states. The results show that the multicanonical algorithm achieves a factor of over two orders of magnitude improvement over the heat bath algorithm, making it a valuable tool for future studies of first-order phase transitions and other statistical mechanics problems.The paper presents a numerical simulation of the first-order phase transition in the 2D 10-state Potts model using the multicanonical Monte Carlo (MC) algorithm. The authors demonstrate that the multicanonical algorithm significantly reduces the computational effort compared to standard heat bath algorithms, especially for large lattice sizes. The tunneling time between metastable states diverges approximately as \( L^{2.65} \), where \( L \) is the linear size of the system, leading to a computational cost of \( V^{2.3} \) per degree of freedom. This improvement is crucial for studying first-order phase transitions, where critical slowing down is a significant issue. The paper also reports a high-precision computation of the interfacial free energy, which is a key quantity in understanding the interface between disordered and ordered states. The results show that the multicanonical algorithm achieves a factor of over two orders of magnitude improvement over the heat bath algorithm, making it a valuable tool for future studies of first-order phase transitions and other statistical mechanics problems.