Table 2 Equivalent energy function for modeling higher order interactions among Ising spins. The second harmonic signal included as a part of the dynamics (not shown here) helps force \(\upphi\) to \(\{0,\uppi \}\).
Order | Ising interaction | Equivalent formulation for constructing dynamical system |
|---|---|---|
2 | \({s}_{i}{s}_{j}\) | \(\mathrm{cos}\left({\phi }_{i}-{\phi }_{j}\right)\) |
3 | \({s}_{i}{s}_{j}{s}_{k}\) | \(\mathrm{cos}\left({\phi }_{i}-{\phi }_{j}+{\phi }_{k}\right)\) |
4 | \({s}_{i}{s}_{j}{s}_{k}{s}_{l}\) | \(\mathrm{cos}\left({\phi }_{i}-{\phi }_{j}+{\phi }_{k}-{\phi }_{l}\right)\) |
5 | \({s}_{i}{s}_{j}{s}_{k}{s}_{l}{s}_{m}\) | \(\mathrm{cos}\left({\phi }_{i}-{\phi }_{j}+{\phi }_{k}-{\phi }_{l}+{\phi }_{m}\right)\) |
6 | \({s}_{i}{s}_{j}{s}_{k}{s}_{l}{s}_{m}{s}_{n}\) | \(\mathrm{cos}\left({\phi }_{i}-{\phi }_{j}+{\phi }_{k}-{\phi }_{l}+{\phi }_{m}-{\phi }_{n}\right)\) |
