Transverse-field Ising square 12x12, open, h = 3

TFIsing/square_144_O_3

Record

-3.1739018(2) E/N (Pauli)

2D Recurrent Neural Network (2DRNN)

Hibat-Allah et al. (2020) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = −∑_⟨ij⟩ σ^z_iσ^z_j − h ∑_i σ^x_i

Transverse field h = 3. Already in Pauli operators, with no S·S term to rescale, so the per-site energy is E/N.

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

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

The record is the lowest eligible energy in this group, and only this group.

E/N (Pauli)	σ	Var(E)	V-score	method	source	year
-3.1739018(2)record	1.9e-7	1.43e-3	9.9e-7	2D Recurrent Neural Network (2DRNN)	Hibat-Allah et al. (2020)	2020
-3.1739009	n/a	9.21e-3	6.3e-6	DMRG (bond dimension = 1024) VarBench reference run	run script, no paper cited	n/a
-3.173799(4)	4.2e-6	3.67e-1	2.5e-4	RBM (alpha = 1) VarBench reference run	run script, no paper cited	n/a
-3.173711(5)	5.1e-6	5.49e-1	3.8e-4	Jastrow baseline VarBench reference run	run script, no paper cited	n/a

Newest published number here: 2020. Nothing has been added to this instance since the VarBench snapshot of 2024-10-22.