The XY model is a kind of classical spin model, in which the spins can rotate in the lattice plane. The XY model is related to physical phenomena including broken-symmetry transitions, superfluid thin films, superconductors, etc. Since it is hard to realize a photonic simulator with high dimensionality and reconfigurability for XY models, the authors proposed a new architecture of the photonic XY simulator based on eigendecomposition. In the photonic simulator, the spin angles are encoded on the phase term of the light field, and the Hamiltonian of arbitrary XY models within the dimensionality limit can be mapped to the output light intensity via an optical vector-matrix multiplication system that can perform arbitrary complex matrix transformations, hence the calculation of the XY Hamiltonian is accelerated. Besides, various tasks can be performed with different configurations in the electronic domain. The Berezinskii-Kosterlitz-Thouless transition of the 400-spin two-dimensional XY model and the ground-state search of two randomly generated XY models are experimentally demonstrated, and the average fidelity of the output intensity vectors is larger than 0.99. This architecture would provide an alternative approach to investigate XY models with photonic systems. This work was published in Physical Review Applied with the title “Programmable and reconfigurable photonic simulator for classical XY models” on August 1^st, 2024 (https://doi.org/10.1103/PhysRevApplied.22.L021001). The first author is Ph.D candidate Jiayi Ouyang, and the corresponding author is Prof. Xue Feng.