Phase transition in a nonlinear optical Ising machine

Many optimization problems such as the traveling salesman problem and number partitioning can be usually solved by finding the ground state of the classical spin model. Realizing an optical Ising machine and demonstrating its optical advantage are currently attracting broad attention in optical physics. We have explored the phase transition in a recently engineered nonlinear optical Ising machine. By tuning the nonlinear interaction, we find that the ferromagnetic to paramagnetic phase transition changes from second-order to first-order due to the competition of different types of spin interactions. Our results provide a deeper theoretical understanding of the nonlinear optical Ising machine and its potential application for addressing optimization problems.