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Randomly removing interlayer bonds drives a spin-1/2 bilayer from Néel order through a Mott glass to a gapped state.

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Random interlayer bond dilution in a bilayer Heisenberg antiferromagnet produces a two-step transition: Néel to Mott glass to quantum disordered, with stretched-exponential susceptibility in the glass phase.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Genuinely new disorder realization with a credible Néel–MG transition; the MG–QD boundary is a crossover estimate the abstract overstates. the 3 major comments →

arxiv 2509.03604 v1 pith:OUAEWPEE submitted 2025-09-03 cond-mat.str-el cond-mat.stat-mech

Mott Glass and Criticality in a S=1/2 Bilayer Heisenberg Model with Interlayer Bond Dilution

Kunpeng Li , Han-Qing Wu , Dao-Xin Yao This is my paper
classification cond-mat.str-el cond-mat.stat-mech MSC 82B2082B2782B44 PACS 75.10.Jm75.40.Mg
keywords bilayer Heisenberg modelquantum Monte Carlobond dilutionMott glassdisordered quantum phase transitionstretched-exponential susceptibilityHarris criterionrare regions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

Using stochastic series expansion quantum Monte Carlo simulations, this paper asks what happens to a spin-1/2 bilayer antiferromagnet when the bonds connecting the two layers are randomly removed. It argues that random interlayer bond dilution produces a two-step transition as the interlayer coupling grows: Néel order first gives way to a gapless, magnetically disordered Mott glass phase, and that phase then gives way to a gapped quantum disordered (dimerized) state. The identifying signature of the intermediate phase is a stretched-exponential uniform susceptibility, χu ~ exp(−b/T^α) with 0 < α < 1, which the paper traces to rare regions of partially decoupled antiferromagnetic clusters. Regular periodic dilution, by contrast, leaves the clean O(3) universality class unchanged (ν ≈ 0.71, β ≈ 0.366, z = 1), while random dilution changes the Néel-to-glass critical exponents in the direction the Harris criterion predicts. If right, this establishes a simple spin-only route to Mott glass physics and gives a concrete observable prediction for disordered bilayer magnets.

Core claim

The paper's central claim is that diluting only the interlayer bonds of a square-lattice S=1/2 bilayer Heisenberg model—keeping every spin site and all intralayer bonds—creates a distinct sequence of ground states as the interlayer coupling ratio g grows. For random dilution at probability P, the system first undergoes a Néel-to-Mott-glass quantum phase transition; at P=0.2 this occurs at g_c=4.201(1) with correlation-length exponent ν=1.01(1), dynamical exponent z=1.236(6), and order-parameter exponent β=0.504(2), clearly different from the clean O(3) values and consistent with disorder being relevant by the Harris criterion. In the intermediate phase, the uniform susceptibility follows a s

What carries the argument

The central object is randomly diluted interlayer bonds in a bilayer Heisenberg model, with dilution probability P and weakened coupling δJ2, which preserves all spin sites while creating isolated antiferromagnetic clusters. The argument is carried by three numerical probes: the Binder ratio and spin stiffness, whose finite-size crossings and data collapses locate the Néel-to-glass transition and its exponents; the staggered magnetization, which provides β; and the temperature dependence of the uniform susceptibility, whose crossover from linear to activated or stretched-exponential behavior in 1/T distinguishes the quantum critical point, the Mott glass, and the gapped phase. The stretched-

Load-bearing premise

The second transition, from Mott glass to quantum disordered phase, rests on assuming that the stretched-exponential exponent α(g) increases linearly with coupling and that α=1 marks the boundary; this is fitted from a narrow g window at a single lattice size (L=32).

What would settle it

Run the same susceptibility analysis on larger lattices (L=48 and 64) and at additional g values near α=1. If the fitted α(g) bends away from the linear extrapolation, or if the inferred boundary shifts systematically with L, the claimed Mott-glass-to-quantum-disordered transition collapses to a crossover. A direct check would be to measure the spin gap: the transition point should coincide with the coupling where the gap opens.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If random dilution is the relevant perturbation, the Néel-to-glass transition in this family of models should not be described by the clean three-dimensional O(3) exponents; the paper's fitted values (ν ≈ 1.0, z ≈ 1.2, β ≈ 0.5) are the quantitative prediction to check.
  • The stretched-exponential susceptibility is a concrete experimental fingerprint: a disordered bilayer magnet should show χu ~ exp(−b/T^α) over a window of interlayer coupling, with α approaching 1 as the spin gap opens.
  • Because the Mott glass and quantum disordered phases are both incompressible and lack long-range order, the second boundary is not a conventional sharp transition; the paper predicts a broad crossover that will not produce Binder-ratio crossings.
  • The critical coupling grows steeply as dilution approaches the site percolation threshold P_c=0.407, suggesting that for sufficiently strong bond dilution Néel order persists to arbitrarily large interlayer coupling.

Where Pith is reading between the lines

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

  • The paper attributes the stretched exponential to a power-law distribution of partially decoupled cluster sizes but does not directly measure that distribution. One extension would be to compute cluster statistics from the quenched bond configurations and test whether the fitted α(g) tracks the percolation cluster-size exponent τ predicted by the rare-region argument.
  • Because the model keeps all spin sites, it offers a cleaner test of Mott-glass behavior without explicit particle-hole symmetry than dimer-diluted models. A natural next step is to add a magnetic field and measure the compressibility analogue, which should stay zero in both glass and disordered phases if the mapping to disordered bosons holds.
  • In real bilayer nickelates, apical oxygen vacancies are a plausible realization of random interlayer bond weakening. If the mechanism is robust, uniform susceptibility measurements on such materials should reveal stretched-exponential behavior in a finite coupling window, whereas regular structural modulations would not.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies the S=1/2 antiferromagnetic Heisenberg bilayer with diluted interlayer couplings using SSE-QMC. For regular dilution patterns, it finds that the Néel-to-quantum-disordered transition remains in the O(3) universality class (ν≈0.71, β≈0.366, z=1), with phase boundaries that shift with dilution. For random interlayer-bond dilution, it claims a two-step transition: Néel to an intermediate Mott glass (MG) phase, and then to a gapped quantum disordered (QD) phase. The MG phase is identified through a stretched-exponential uniform susceptibility χu ∼ exp(−b/T^α) with 0<α<1. At the Néel–MG transition, disorder-modified critical exponents are reported (e.g., for P=0.2, gc=4.201(1), ν=1.01(1), z=1.236(6), β=0.504(2)). The MG–QD boundary is located by fitting α(g) linearly and extrapolating to α=1.

Significance. If established, the paper would provide a clean example of a disorder-driven intermediate gapless nonmagnetic phase in a purely spin model where all spin sites are preserved, extending earlier Mott-glass studies in dimer-diluted and single-layer models. The regular-dilution results are a useful systematic benchmark, and the finite-size scaling of the Néel–MG transition is a solid contribution. The paper also makes a concrete, falsifiable prediction for the temperature dependence of the uniform susceptibility. Its main strength is the combination of multiple observables (Binder ratio, spin stiffness, staggered magnetization, and susceptibility) with SSE-QMC up to L=64 for the clean/regular cases. However, the central two-step phase diagram is not fully supported: the evidence for the second transition rests on a single-size, single-observable extrapolation, and the manuscript itself concedes the boundary may be a broad crossover.

major comments (3)
  1. [Sec. IV.B, Fig. 11 inset] The MG–QD boundary is determined by fitting the stretched-exponential exponent α(g) to a linear function and extrapolating to α=1. There is no theoretical reason for α(g) to be linear, the data are for L=32 only, and the number of disorder realizations is not stated. The manuscript itself (Sec. IV, paragraph before IV.A) says this boundary 'lacks a sharp finite-size signature' and 'likely proceeds via a broad crossover,' yet the abstract and Sec. V present it as a distinct transition. This is load-bearing: without the second boundary, the claimed two-step picture reduces to a single Néel–MG transition plus a crossover. Please provide robustness checks (larger L, multiple disorder realizations, alternative functional forms, or a physically motivated argument for linearity) or soften the central claim.
  2. [Sec. IV.A, Eq. (8), Table II] The 'independent' check of the dynamical exponent z via χu(T) is not fully independent: it uses the same assumed scaling form χu = a + bT^{d/z−1} and the same critical coupling gc inferred from the same data set. More importantly, Table II is headed 'P=0.2, δ=0.4' while the text and Hamiltonian use δ=0 for the random case. If this is a typo, it should be corrected; if not, the simulations need clarification. The number of disorder realizations underlying the averages and error bars should also be reported, since disorder-averaged QMC results are otherwise difficult to assess.
  3. [Sec. IV.A, Table II and Fig. 9] The three observables give gc = 4.23(6), 4.17(6), and 4.11(2), while the finite-size drift analysis yields gc(∞)=4.201(1). The quoted precision of 0.001 appears to ignore the observable-dependent scatter. Please explain how the common gc is obtained from these values and how the final error bar accounts for systematic differences between observables and extrapolation choices.
minor comments (5)
  1. [Eq. (1)] The interlayer interaction terms are written as 'Si,1Si,2' without dot products; use Si,1·Si,2 for clarity.
  2. [Sec. II.A heading] 'Halmitonian' should be 'Hamiltonian'.
  3. [Sec. V] The text contains 'N’eel-ordered' with a curly apostrophe; use 'Néel-ordered'.
  4. [Sec. IV.A] 'should not be fixed priories' should read 'should not be fixed a priori'.
  5. [Sec. IV.B] The phrase 'typical of of the quantum-disordered phase' contains a duplicated 'of'.

Circularity Check

1 steps flagged

Second (MG-QD) transition is defined by α=1 and then located by fitting α(g), so that boundary is a fitted definition rather than an independently detected phase transition.

specific steps
  1. self definitional [Section IV.B (Uniform Susceptibility and Mott Glass–Quantum Disordered Crossover), near Eq. (16) and inset of Fig. 11]
    "The exponent α in the stretched-exponential behavior increases with g and approaches unity in the quantum-disordered regime. This trend enables a systematic analysis of α(g) to identify the phase boundary between the Mott glass and quantum-disordered phase. We find that α exhibits a linear dependence on g, which allows us to perform a linear fit and extract the critical coupling by locating the point where α = 1."

    The MG phase is defined by 0<α<1 through Eq. (16), while the QD phase is defined by activated behavior with α=1 (Eq. 15). The paper then 'identifies' the MG-QD boundary by fitting α(g) and setting α=1. Since α is the same fitting parameter extracted from the χu(T) data used to assign the phase, the boundary is a restatement of the classification criterion rather than an independent determination. The linear extrapolation of α(g) is an additional unvalidated ansatz, and the paper itself concedes the transition 'lacks a sharp finite-size signature' and 'likely proceeds via a broad crossover' (Sec. IV). Thus the abstract's 'second transition' reduces to a fitted-α definition.

full rationale

The Néel–Mott-glass boundary is determined by standard finite-size scaling of the Binder ratio, spin stiffness, and staggered magnetization, with critical exponents cross-checked internally; that part of the derivation is independent and not circular. Self-citations to Refs. [23,26] report similar Mott-glass behavior, but the present identification is supported by the paper's own χu(T) fits, so those citations are not load-bearing. The circularity is confined to the second boundary: the MG and QD phases are defined by the value of the stretched-exponential exponent α, and the MG-QD boundary is then located by fitting α(g) and taking α=1. This is a definitional construction plus a linear-fit extrapolation, not a detection of a true transition via an independent order parameter or diverging scale. Because one of the two claimed transitions is thus not independently derived, but the Néel-MG transition and the stretched-exponential data provide real independent content, the score is 6 rather than 8 or 10.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper introduces no new particles, forces, or conserved quantities. The free parameters are all fitting constants in the stretched-exponential analysis and the finite-size correction extrapolations. The axiomatic input is the validity of SSE-QMC at the chosen beta, the applicability of rare-region scaling arguments from prior work, and the Harris criterion, all standard assumptions for this class of numerical study.

free parameters (4)
  • b (stretched exponential prefactor) = varies with g
    Fitted to chi_u(T) using the form exp(-b/T^alpha) in Eq. (16); the MG-QD boundary analysis depends on these fits.
  • alpha (stretched exponential exponent) = varies with g, between 0 and 1
    Extracted from chi_u(T) data for each g; this is the parameter used to define the Mott glass phase and to extrapolate the MG-QD boundary.
  • linear fit slope and intercept of alpha(g) = not reported numerically
    Used in Section IV.B and Fig. 11 inset to locate the MG-QD transition at alpha=1; the phase boundary is therefore a fitted quantity.
  • correction exponent omega = 1.950(1) for rho_s, 2.220(1) for R2 in the 1/2 regular pattern
    Appears in Eq. (11) for the finite-size extrapolation of the critical coupling gc(L); it is treated as an adjustable fitting parameter.
axioms (4)
  • domain assumption SSE-QMC at beta=2L accurately represents ground-state properties for L up to 64.
    This is standard practice in the field, but the paper does not demonstrate convergence in beta beyond this choice.
  • domain assumption The rare-region cluster argument from Ref. [33] applies to this interlayer-diluted model.
    In Section IV.B the stretched-exponential chi_u is interpreted using cluster-size distributions and gap scaling from Ref. [33]; no derivation is given for this specific model.
  • domain assumption The Harris criterion applies with d=2 (spatial dimension only).
    Invoked in the Introduction and Section IV to infer that disorder is relevant because the clean nu=0.71 is less than 2/d=1.
  • standard math Percolation cluster-size distribution P(s) ~ s^-tau below the percolation threshold.
    Used in Section IV.B to justify the MG phase; this is standard percolation theory, but the connection to the quantum gap scaling is assumed.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Mott Glass and Criticality in a S=1/2 Bilayer Heisenberg Model with Interlayer Bond Dilution." pith.science (2026). https://pith.science/paper/OUAEWPEE

@misc{pith2026250903604,
  author       = {Pith},
  title        = {Pith review of: Mott Glass and Criticality in a S=1/2 Bilayer Heisenberg Model with Interlayer Bond Dilution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OUAEWPEE}},
  note         = {Machine review of arXiv:2509.03604}
}
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abstract

We employ the stochastic series expansion quantum Monte Carlo (SSE-QMC) method to investigate the $S = 1/2$ antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a N\'eel-ordered phase to a quantum disordered phase, consistent with the $O(3)$ universality class. In contrast, random dilution gives rise to a two-step transition: from the N\'eel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence $\chi_u \sim \exp(-b/T^\alpha)$, $0 < \alpha < 1$. At the N\'eel-to-glass transition, quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum spin-glass criticality in disordered frustrated dimer magnets

    cond-mat.str-el 2026-07 conditional novelty 6.0

    In a disordered triangular bilayer Heisenberg magnet, theory predicts a quantum spin glass whose near-critical order is sparse and nearly collinear — 'doubly weak' — with strongly suppressed amplitude (Higgs) mode weight.

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.