  Recently, spatial photonic Ising machines (SPIM) have been demonstrated to
compute the minima of Hamiltonians for large-scale spin systems. Here we
propose to implement an antiferromagnetic model through optoelectronic
correlation computing with SPIM. Also we exploit the gauge transformation which
enables encoding the spins and the interaction strengths in a single phase-only
spatial light modulator. With a simple setup, we experimentally show the ground
state search of an antiferromagnetic model with $40000$ spins in
number-partitioning problem. Thus such an optoelectronic computing exhibits
great programmability and scalability for the practical applications of
studying statistical systems and combinatorial optimization problems.
