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Critical slowing down of topological modes

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arxiv hep-lat/0403001 v1 pith:BQAHKK7D submitted 2004-03-01 hep-lat

classification hep-lat
keywords modestopologicalcriticaldownlatticeslowingcarlomonte
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We investigate the critical slowing down of the topological modes using local updating algorithms in lattice 2-d CP^(N-1) models. We show that the topological modes experience a critical slowing down that is much more severe than the one of the quasi-Gaussian modes relevant to the magnetic susceptibility, which is characterized by $\tau_{\rm mag} \sim \xi^z$ with $z\approx 2$. We argue that this may be a general feature of Monte Carlo simulations of lattice theories with non-trivial topological properties, such as QCD, as also suggested by recent Monte Carlo simulations of 4-d SU(N) lattice gauge theories.

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Forward citations

Cited by 9 Pith papers

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

  1. The topological susceptibility slope $\chi^\prime$ in the large-$N$ limit

    hep-lat 2026-06 unverdicted novelty 8.0 of 10

    First non-perturbative lattice determination of the Yang-Mills topological susceptibility slope χ' in the large-N limit using a novel algorithm to avoid topological freezing.

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  3. Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory

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    Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.

  4. Exploring Generative Networks for Manifolds with Non-Trivial Topology

    hep-lat 2025-02 reject novelty 6.0 of 10

    A GFlowNet-inspired diffusion sampler is proposed and shown, on toy and 2D lattice scalar models, to generate configurations across disconnected sectors that normalizing flows and plain diffusion models miss.

  5. Parallel Tempered Metadynamics for full QCD

    hep-lat 2026-07 conditional novelty 5.0 of 10

    In N_f=2 staggered QCD at beta=1.15, PT-MetaD tunnels between topological sectors while RHMC remains frozen, yielding chi_top V = 0.127(33).

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    hep-lat 2025-11 unverdicted novelty 5.0 of 10

    Gradient-flow scales are set for SU(3), SU(5), SU(8) and large-N Yang-Mills down to 0.025 fm using twisted volume reduction and topology-taming algorithms.

  7. Bounding statistical errors in lattice field theory simulations

    hep-lat 2025-06 unverdicted novelty 5.0 of 10

    Introduces bounds-based stopping criteria and automatic windowing for autocorrelation integrals to estimate statistical errors in lattice field theory Monte Carlo simulations.

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    hep-lat 2025-01 conditional novelty 5.0 of 10

    Using twisted boundary conditions and parallel tempering, the SU(5) gradient-flow scale sqrt(t0) is measured at three lattice spacings, with the topological freezing bias vanishing in the infinite-volume limit.

  9. Lattice techniques to investigate the strong $CP$ problem: lessons from a toy model

    hep-lat 2025-02 accept novelty 4.0 of 10

    In a quantum rotor with a topological term, the proposed order of limits predicts zero topological susceptibility, contradicting both the exact quantum mechanical result and lattice simulations.

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