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arxiv: 2605.28761 · v1 · pith:UVHXCJLInew · submitted 2026-05-27 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Avoided Stoner instability at a single ordinary Van Hove point

I.S. Tupitsyn , B. Currie , A.V. Chubukov , B.V. Svistunov , E. Kozik , N.V. Prokof'ev This is my paper

Pith reviewed 2026-06-29 09:45 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords Hubbard modelVan Hove singularityStoner instabilityferromagnetismdiagrammatic Monte Carloquasiparticle residuetwo-dimensional systems
0
0 comments X

The pith

In the 2D Hubbard model at an ordinary Van Hove point, the ferromagnetic Stoner instability is avoided down to temperatures an order of magnitude below the mean-field prediction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Mean-field theory predicts a ferromagnetic Stoner instability at finite temperature for any coupling strength when the Fermi surface touches the Brillouin zone boundary at a Van Hove point, because the density of states diverges. This prediction has not been seen in experiments. Numerically exact diagrammatic Monte Carlo calculations on the two-dimensional Hubbard model show that the instability is suppressed by a downward renormalization of the effective coupling together with a reduction in the density of states from loss of quasiparticle residue. A reader would care because the result accounts for the mismatch between mean-field expectations and actual behavior in systems with Van Hove singularities.

Core claim

When the Fermi surface and the Brillouin zone boundary touch at a Van Hove point, mean-field analysis predicts a ferromagnetic (Stoner) instability at finite T_MF for any coupling strength due to the divergent density of states. However, in the two-dimensional Hubbard model with an ordinary Van Hove singularity, two diagrammatic Monte Carlo approaches demonstrate that the system avoids the Stoner instability down to temperatures an order of magnitude below T_MF. The suppression arises from the combination of the downward renormalization of the effective coupling and the suppression of the density of states by the loss of the quasiparticle residue.

What carries the argument

Diagrammatic Monte Carlo methods (four-channel self-consistent approximation and combinatorial summation with controlled resummation) applied to the Hubbard model at the Van Hove point, which track renormalization of the coupling and quasiparticle residue.

If this is right

  • The effective coupling constant is renormalized downward at low temperatures.
  • The quasiparticle residue drops, which directly reduces the effective density of states.
  • No ferromagnetic instability appears until temperatures are at least an order of magnitude below the mean-field scale.
  • This combination of effects accounts for the experimental absence of the predicted Stoner transition.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same suppression mechanisms may operate at other Van Hove singularities or in models with longer-range interactions.
  • Numerical studies of doped cuprate-like band structures could check whether the avoided instability persists away from half-filling.
  • Analytic resummation techniques might be developed to capture the same renormalization without full Monte Carlo sampling.

Load-bearing premise

The two diagrammatic Monte Carlo methods remain accurate and free of uncontrolled truncation errors when applied to the Hubbard model at the Van Hove point.

What would settle it

Observation of ferromagnetic ordering at a temperature close to the mean-field T_MF in a two-dimensional Hubbard-like system tuned exactly to an ordinary Van Hove point would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.28761 by A.V. Chubukov, B. Currie, B.V. Svistunov, E. Kozik, I.S. Tupitsyn, N.V. Prokof'ev.

Figure 1
Figure 1. Figure 1: FIG. 1. Fermi surfaces of the interacting (solid lines) and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Bold4+ approximation results for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Bold4+ results for the frequency dependence of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. DiagMC-CoS results for [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Static magnetic susceptibility [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
read the original abstract

When the Fermi surface and the Brillouin zone boundary touch at a Van Hove point, mean-field analysis predicts a ferromagnetic (Stoner) instability at finite $T_{MF}$ for any coupling strength due to the divergent density of states. However, the predicted effect has not been observed experimentally. Several qualitative theoretical proposals have been put forward to explain why the mean-field prediction fails. Based on numerically exact results for the two-dimensional Hubbard model with an ordinary Van Hove singularity, we uncover the mechanisms behind the suppression of the ferromagnetic instability. We employ two diagrammatic Monte Carlo approaches: (i) the four-channel self-consistent approximation and (ii) numerically exact method of combinatorial summation of diagrams with controlled resummation of the truncated expansion. We find that the system avoids the Stoner instability down to temperatures an order of magnitude below $T_{MF}$ due to the combination of the downward renormalization of the effective coupling and the suppression of the density of states by the loss of the quasiparticle residue.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims that for the 2D Hubbard model at an ordinary Van Hove singularity, mean-field theory predicts a Stoner ferromagnetic instability at finite T_MF for any U>0 due to divergent DOS, but two diagrammatic Monte Carlo methods (four-channel self-consistent approximation and combinatorial diagram summation with controlled resummation) show the instability is avoided down to T ≪ T_MF. The mechanisms are downward renormalization of the effective interaction plus suppression of the DOS by loss of quasiparticle residue Z.

Significance. If the central claim holds, the work supplies a concrete, non-perturbative explanation for the experimental absence of Stoner ferromagnetism near Van Hove points and demonstrates how diagrammatic resummation captures the interplay of coupling renormalization and Z suppression in a logarithmically divergent DOS. The deployment of two independent controlled diagrammatic Monte Carlo schemes is a methodological strength.

major comments (1)
  1. [Methods (diagrammatic Monte Carlo sections)] The assertion of 'numerically exact' results (abstract and methods description) is load-bearing for the claim that the Stoner instability is avoided. At the Van Hove point the bare DOS diverges, which can slow diagrammatic convergence; yet the manuscript provides no explicit order-by-order residuals, convergence tables, or quantitative cross-validation between the four-channel self-consistent approximation and the combinatorial summation at the lowest temperatures reported.
minor comments (1)
  1. Notation for the effective coupling and the quasiparticle residue Z should be introduced with a single equation reference when first used in the results discussion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need for explicit convergence documentation to support the claim of numerically exact results. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Methods (diagrammatic Monte Carlo sections)] The assertion of 'numerically exact' results (abstract and methods description) is load-bearing for the claim that the Stoner instability is avoided. At the Van Hove point the bare DOS diverges, which can slow diagrammatic convergence; yet the manuscript provides no explicit order-by-order residuals, convergence tables, or quantitative cross-validation between the four-channel self-consistent approximation and the combinatorial summation at the lowest temperatures reported.

    Authors: We agree that explicit documentation of convergence is necessary to substantiate the 'numerically exact' characterization, especially given the divergent DOS at the Van Hove point. The combinatorial summation employs a controlled resummation with an explicit truncation-error estimator, and the two independent methods produce consistent results for the key observables. Nevertheless, the original manuscript did not include order-by-order residuals or quantitative cross-validation tables at the lowest temperatures. In the revised version we will add (i) tables and plots of residuals versus diagram order at the lowest reported temperatures for both methods, (ii) a direct quantitative comparison of the two methods' outputs at those temperatures, and (iii) a brief discussion of how the resummation procedure remains stable despite the divergent bare DOS. These additions will directly address the referee's concern. revision: yes

Circularity Check

0 steps flagged

No circularity: central results obtained from direct numerical summation on the Hubbard model

full rationale

The paper reports its key findings—the avoidance of Stoner instability down to T ≪ T_MF via coupling renormalization and Z suppression—explicitly as outcomes of two diagrammatic Monte Carlo techniques applied to the 2D Hubbard model at the Van Hove point. No analytical derivation chain exists that reduces a claimed prediction to a fitted parameter, self-defined quantity, or self-citation loop; the methods are presented as numerically exact computational tools whose outputs constitute the evidence. The abstract and described approach contain no instances of self-definitional relations, fitted inputs relabeled as predictions, or load-bearing uniqueness theorems imported from prior author work. This is the standard case of a self-contained numerical study whose validity rests on method convergence rather than internal definitional equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard Hubbard model Hamiltonian and the accuracy of the two diagrammatic Monte Carlo techniques; no new entities are introduced and no parameters are fitted to produce the reported suppression.

axioms (1)
  • domain assumption The Hubbard model on a square lattice with nearest-neighbor hopping accurately captures the low-energy physics near an ordinary Van Hove singularity.
    Standard modeling choice for 2D interacting electrons invoked to justify the choice of Hamiltonian.

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