Spatial Optical Simulator for Classical Statistical Models

TL;DR

This paper presents a spatial optical simulator using a digital micromirror device to model various classical statistical systems, enabling the study of phase transitions and complex interactions with high precision.

Contribution

The authors develop a versatile optical simulation platform for multiple classical models, preserving Hamiltonian symmetries and simulating complex interactions on fully connected networks.

Findings

Successfully simulated phase transitions in Ising, XY, Potts, and Heisenberg models.

Demonstrated the simulator's ability to handle ferromagnetic and spin-glass interactions.

Extended the scope of optical simulators to a broader class of statistical models.

Abstract

Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock, $XY$, Potts, and Heisenberg models, utilizing a digital micromirror device composed of a large number of tiny mirrors. Spins, with desired amplitudes or phases of the statistical models, are precisely encoded by a patch of mirrors with a superpixel approach. Then, by modulating the light field in a sequence of designed patterns, the spin-spin interaction is realized in such a way that the Hamiltonian symmetries are preserved. We successfully simulate statistical systems on a fully connected network, with ferromagnetic or Mattis-type random interactions, and observe the corresponding phase transitions between the paramagnetic, and the ferromagnetic or spin-glass phases. Our results largely extend the research scope of spatial optical simulators and their versatile applications.