Astroid Spinodal Boundary in Phase-Based Ising Machines

Malihe Farasat; Nikhil Shukla

Astroid Spinodal Boundary in Phase-Based Ising Machines

Computational Physics 2026-07-28 v1

Authors: Malihe Farasat , Nikhil Shukla

Abstract

Oscillator Ising machines (OIMs) and dynamical Ising machines (DIMs) encode binary spins in phase states stabilized by second-harmonic injection (SHI). In a coupled network, the competition between SHI and the instantaneous local network field reshapes each oscillator's conditional energy landscape. We show that this competition drives a transition between monostable and bistable regimes through an astroid spinodal boundary. Near this boundary, the barrier scales as $\Delta E_i\propto\mu_i^{3/2}$ at generic smooth points and as $\Delta E_i\propto\mu_i^{2}$ at the longitudinal cusp. OIMs and DIMs obey the same spinodal geometry, with their conditional landscapes related by a reversal of the transverse field. Finally, the first-harmonic conditional landscape is mathematically equivalent, up to an additive constant, to the Stoner--Wohlfarth energy of a uniaxial magnetic particle.

Cite

@article{arxiv.2607.26213,
  title  = {Astroid Spinodal Boundary in Phase-Based Ising Machines},
  author = {Malihe Farasat and Nikhil Shukla},
  journal= {arXiv preprint arXiv:2607.26213},
  year   = {2026}
}