The Hamiltonian
H = ∑⟨ij⟩ σi·σj + J2 ∑⟨⟨ij⟩⟩ σi·σj
J1 = 1, J2 = 0.2, nearest and next-nearest neighbours, written with Pauli matrices.
- lattice
- honeycomb-7x7
- sites
- 98
- boundary
- periodic
- J2
- 0.2
- energies
- 4
Stored as a total energy; quoted here as
E/N (S.S), which is what the papers report
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-0.4538(4), VMC (LCN)
Checked 2026-10-20 · source text of arXiv:2206.07370 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)
Reported as. -0.4538(4)
Table 1, Honeycomb N = 98, J2 = 0.2, column LCN; version read: arXiv text (sources/2206.07370.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Same Hamiltonian, lattices and references as arXiv:2110.06390 (Sec. 'Lattice': 'Following Kochkov et al. [27]'); Table 1 'energy per site'.
-0.4536(5), VMC (GNN)
Checked 2026-10-20 · source text of arXiv:2110.06390 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)
Reported as. -0.4536(5)
Table IV, Honeycomb, J2 = 0.2, N = 98, column GNN-2; version read: arXiv text; no journal version found (arXiv metadata) | Eq. (4) H = sum S_i.S_j + J2 sum S_i.S_j, spin-1/2, J1 = 1; Table IV '<E>/N', 'variational energies per spin'.
-0.4528(2), VMC (GNN)
Checked 2026-10-20 · source text of arXiv:2110.06390 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)
Reported as. -0.4528(2)
Table IV, Honeycomb, J2 = 0.2, N = 98, column GNN; version read: arXiv text; no journal version found (arXiv metadata) | Eq. (4) H = sum S_i.S_j + J2 sum S_i.S_j, spin-1/2, J1 = 1; Table IV '<E>/N', 'variational energies per spin'.
-0.4496(4), VMC (ResNet)
Checked 2026-10-20 · source text of arXiv:2110.06390 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)
Reported as. -0.4496(4)
Table IV, Honeycomb, J2 = 0.2, N = 98, column ResNet; version read: arXiv text; no journal version found (arXiv metadata) | Eq. (4) H = sum S_i.S_j + J2 sum S_i.S_j, spin-1/2, J1 = 1; Table IV '<E>/N', 'variational energies per spin'.