J1-J2 square 18x18, J2 = 0.44

No record

—

sampled rows carry no error bar (rules §6). Every row is still listed below.

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j + J₂ ∑_{⟨⟨ij⟩⟩} σ_i·σ_j

J₁ = 1, J₂ = 0.44, nearest and next-nearest neighbours, written with Pauli matrices.

lattice: square
sites: 324
boundary: periodic
J2: 0.44
energies: 1

Stored as a total energy in the convention of VarBench; quoted here as E/N (S.S), which is what the papers report (how the conversion works).

Every published energy

Grouped by what the number is. Ranking happens only inside the first group.

Strict variational upper bounds (1)

Where the instance is not solved, the record is the lowest eligible energy in this group; where it is, the lowest eligible energy here is the best variational bound and the closest challenger to the exact one.

E/N (S.S)	distance to record	σ	Var(E)	V-score	method	source	year
-0.5117900	n/a	n/a	n/a	n/a	CNN peer reviewed ineligible: sampled, no error bar	10.1109/TPDS.2022.3145163,	2022

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.5117900 — CNN

Checked 2026-10-07 · source text of arXiv:2108.13830 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading

Reported as. -0.51179

Table 4 ('Energies for varied J2/J1 && system scales'), row 18 x 18, column 0.44; no error bar printed | Energy per site in S.S units, periodic boundary conditions (text: 'periodic boundary condition'); the 10x10 and 16x16 cells at J2 = 0.50 equal the rows QMBL already carries from this table.

Coverage

Newest published number here: 2022. 1 row added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

JSON · source file on GitHub · open an issue about this instance