  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.
