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arxiv: 2606.21217 · v1 · pith:MZ2OGWIQnew · submitted 2026-06-19 · ✦ hep-lat

Event-Chain Monte Carlo for Yang-Mills SU(N) lattice field theory I : Design and proof of concept

Beno\^it Blossier , Manon Michel , Yacob Ozdalkiran This is my paper

Pith reviewed 2026-06-26 12:52 UTC · model grok-4.3

classification ✦ hep-lat
keywords event-chain Monte Carlolattice gauge theoryYang-MillsSU(N)Wilson actionirreversible Markov processglobal balance
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The pith

Event-chain Monte Carlo produces irreversible rejection-free dynamics that sample the Wilson gauge measure for SU(N) lattice theories.

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

The paper develops two ECMC implementations for Yang-Mills SU(N) theories with the Wilson action. These consist of sequences of local ballistic updates separated by stochastic events that generate an irreversible Markov chain. The dynamics are constructed to obey global balance and therefore converge to the correct equilibrium distribution. Numerical runs on four-dimensional lattices for N=3 recover the same mean plaquette values obtained from standard Monte Carlo methods.

Core claim

Two explicit ECMC schemes for general SU(N) Yang-Mills with Wilson action are formulated; each is built from local ballistic updates interrupted by stochastic events, yields an irreversible rejection-free process, satisfies global balance, and reproduces conventional Monte Carlo results for gauge observables on four-dimensional lattices when tested at N=3.

What carries the argument

Succession of local ballistic updates interspersed with stochastic events that together enforce global balance while remaining rejection-free.

If this is right

  • The algorithm supplies a rejection-free dynamics for SU(N) lattice gauge theories.
  • Global balance is preserved, so the equilibrium distribution remains exact.
  • The same construction applies to any N without modification of the update rules.
  • Standard observables such as the mean plaquette are recovered on four-dimensional volumes.

Where Pith is reading between the lines

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

  • The irreversible character may reduce autocorrelation times relative to reversible Metropolis updates.
  • Extension to improved actions would require redesign of the stochastic-event rules while preserving global balance.
  • The method could be combined with existing gauge-fixing or fermion-update techniques once the pure-gauge case is validated.

Load-bearing premise

The particular choice of stochastic events for the Wilson action produces a process whose stationary distribution is exactly the desired gauge-theory measure.

What would settle it

A direct numerical comparison in which the long-time average of the plaquette (or any other local gauge-invariant operator) on a fixed four-dimensional lattice differs from the value obtained by a conventional heat-bath or Metropolis algorithm at the same coupling.

read the original abstract

We develop two implementations of the Event-Chain Monte Carlo (ECMC) algorithm for Yang-Mills $\mathrm{SU}(N)$ lattice gauge theories with the Wilson action. These algorithms consist in a succession of local ballistic updates intersped with stochastic events, resulting in an irreversible and rejection-free Markov process. The resulting dynamics satisfy global balance, ensuring the correct equilibrium distribution. The algorithms are formulated for general $\mathrm{SU}(N)$ Yang-Mills theories with Wilson action and implemented for the case $N=3$. Numerical tests on four-dimensional lattices show that standard gauge observables, such as the mean plaquette, agree with results obtained using conventional Monte Carlo algorithms. These results provide a first validation of ECMC as a viable sampling scheme for Yang-Mills lattice gauge theories.

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 / 2 minor

Summary. The paper develops two implementations of the Event-Chain Monte Carlo (ECMC) algorithm for SU(N) Yang-Mills lattice gauge theories with the Wilson action. The algorithms consist of local ballistic updates interspersed with stochastic events, yielding an irreversible rejection-free Markov process. The authors state that the dynamics satisfy global balance and thus sample the correct equilibrium distribution. For N=3 the method is implemented and tested on four-dimensional lattices, where the mean plaquette is reported to agree with results from conventional Monte Carlo algorithms. This constitutes a proof-of-concept validation.

Significance. If the global-balance construction is rigorously established for the non-Abelian Wilson action, the work would represent a non-trivial extension of ECMC to lattice gauge theories. ECMC has previously demonstrated reduced autocorrelation in other systems; a rejection-free irreversible sampler for SU(N) could therefore offer efficiency gains for gauge-field sampling. The numerical agreement for the plaquette on modest lattices provides initial supporting evidence, though the scope remains limited to a single observable and small volumes.

major comments (1)
  1. [algorithm design section] The central claim that the chosen stochastic events enforce global balance for the Wilson action on SU(N) links is load-bearing, yet the explicit event-rate formulas and the verification that they satisfy the global-balance condition (rather than merely being asserted) are not supplied with sufficient detail to allow independent verification of the stationary distribution.
minor comments (2)
  1. The numerical tests are described only at the level of 'agreement' for the mean plaquette; quantitative details (lattice sizes, statistics, error bars, and comparison to a reference method) should be added to make the validation reproducible.
  2. Notation for the link variables and the precise definition of the ballistic updates should be introduced earlier and used consistently throughout.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [algorithm design section] The central claim that the chosen stochastic events enforce global balance for the Wilson action on SU(N) links is load-bearing, yet the explicit event-rate formulas and the verification that they satisfy the global-balance condition (rather than merely being asserted) are not supplied with sufficient detail to allow independent verification of the stationary distribution.

    Authors: We agree that the current manuscript does not supply the explicit event-rate formulas and the step-by-step verification of global balance with enough detail for independent checking. In the revised version we will expand the algorithm design section to derive the full event-rate expressions for the Wilson action on SU(N) links and to present a complete verification that these rates enforce the global-balance condition, thereby confirming the correct stationary distribution. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation validated against independent benchmarks

full rationale

The paper designs ECMC algorithms for SU(N) Wilson Yang-Mills, asserts that the constructed dynamics satisfy global balance, and validates this by direct numerical comparison of observables (e.g., mean plaquette) to results from conventional Monte Carlo on 4D lattices. No equations or claims reduce the target equilibrium measure to a fitted parameter, self-citation, or renamed input; the validation is performed against an external, independent sampling method. This is the normal case of a self-contained algorithmic proposal with external falsifiability.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond the general claim that global balance holds for the constructed dynamics.

axioms (1)
  • domain assumption The stochastic events are chosen so that the irreversible process satisfies global balance and therefore has the Wilson-action measure as its unique stationary distribution.
    Invoked to guarantee correctness of the sampling; location: abstract paragraph describing the Markov process.

pith-pipeline@v0.9.1-grok · 5673 in / 1290 out tokens · 28901 ms · 2026-06-26T12:52:30.359301+00:00 · methodology

discussion (0)

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