Free energy of non-convex multi-species Ising spin glasses with external fields

@misc{boursier2026free,
  title = {{Free energy of non-convex multi-species Ising spin glasses with external fields}},
  author = {Jeanne Boursier and Jean-Christophe Mourrat},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18350},
  eprint = {2610.18350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18350},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Free energy of non-convex multi-species Ising spin glasses with external fields
AU  - Jeanne Boursier
AU  - Jean-Christophe Mourrat
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18350
UR  - https://arxiv.org/abs/2610.18350
AB  - We identify the limit free energy of mean-field multi-species spin glasses with +/-1 spins, allowing for the presence of external fields, and without assuming any convexity property of the covariance function of the Hamiltonian. The limit is given by an "uninverted" variational formula over Brownian martingales. The proof consists in first identifying the limit free energy of configurations with a fixed magnetization. Once the magnetization is fixed, we can show the convergence of the enriched free energy to the solution of a Hamilton-Jacobi equation. The magnetization constraint is also used to show the convexity of the initial condition in this equation, and this yields a variational representation of the solution, as a Hopf formula. Convex duality then turns this formula into an optimization over martingales whose initial values are the prescribed magnetizations.
ER  -