Simulating Ising and Potts models and external fields with non-equilibrium condensates

TL;DR

This paper demonstrates how to simulate Ising and Potts spin models, including external fields, using non-equilibrium condensates like lasers and Bose-Einstein condensates, enabling physical simulation of complex Hamiltonians.

Contribution

It introduces a method to simulate discrete spin models with continuous phase platforms, expanding the scope of physical Hamiltonian simulations.

Findings

Simulation of Ising and Potts models with external fields achieved

Platforms include lasers and Bose-Einstein condensates

Enables study of complex, time-varying Hamiltonians

Abstract

Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we show how to simulate the discrete Ising and Potts models with or without external fields using the physical gain-dissipative platforms with continuous phases such as lasers and various non-equilibrium Bose-Einstein condensates. The underlying operational principle originates from a combination of resonant and non-resonant pumping. Our results lay grounds for the physical simulations of a broad range of Hamiltonians with complex interactions that can vary in time and space and with combined symmetries.