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All instances / J1-J2

J1-J2 square 10x10, J2 = 0.2

Record

-0.592847(9) E/N (S.S)

RBM

Chen et al. (2022) · lowest eligible strict variational bound (rules §6)

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
square
sites
100
boundary
periodic
J2
0.2
energies
3

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 (3)

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)σVar(E)V-score methodsourceyear
-0.5929820 n/a 3.52e-1 6.3e-4 ViT
preprint ineligible: sampled, no error bar
Golubev et al. (2026) 2026
-0.592847(9)record 9.0e-6 n/a n/a RBM
preprint
Chen et al. (2022) 2022
-0.59275(1) 1.0e-5 n/a n/a CNN
quoted from another paper peer reviewed
Choo et al. (2019), quoted in Chen et al. (2022) 2019

How these numbers were read

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

-0.5929820 — ViT

Checked 2026-09-28 · source text of arXiv:2606.04558 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. -0.592982

Table I, row J2=0.20, column '10×10, ViT (this work)' | Table I prints energy per site in S.S units: its J2 = 0 QMC column equals Sandvik's exact values on Heisenberg/square_64_P and square_100_P.

-0.592847(9) — RBM

Checked 2026-09-28 · source text of arXiv:2206.14307 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. -0.592847(9)

Table 5, row 'Energy(RBM)', 10x10 J2 = 0.2 | Energy per site E/N in S.S units (table captions); the 6x6 exact column equals the exact rows QMBL carries.

-0.59275(1) — CNN

Checked 2026-09-28 · source text of arXiv:2206.14307 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. -0.59275(1)

Table 5, row 'Energy(CNN)', 10x10 J2 = 0.2 | Energy per site E/N in S.S units (table captions); the 6x6 exact column equals the exact rows QMBL carries.

Coverage

Newest published number here: 2026. 3 rows 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