Numerical Construction of the Aizenman-Wehr Metastate

Billoire, A.; Fernández, L.A.; Maiorano, Andrea; Marinari, Enzo; Martı́n-Mayor, V.; Moreno-Gordo, J.; Parisi, G.; Ricci-Tersenghi, Federico; Ruiz‐Lorenzo, J. J.

doi:10.1103/physrevlett.119.037203

Cited by 19 publications

(28 citation statements)

References 58 publications

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“…( 22), as a function of lattice size for three representative interactions σ ∈ {0.625, 0.720, 0.896}. For each coupling multiple lattice sizes N ∈ 2 10 , 2 14 , 2 18 , 2 22 , 2 24 , 2 26 were simulated to investigate finite-size effects. We see from panel (c) of Fig.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range

Jensen,

Read,

Young

2021

Preprint

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Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature Tc for a one-dimensional Ising spin glass model with diluted long-range interactions. In this model, the probability Pij that an edge {i, j} has nonvanishing interaction falls as a power-law with chord distance, Pij ∝ 1/R 2σ ij , and we study a range of values of σ with 1/2 < σ < 1. We consider a correlation function C4(r, t). A dynamic correlation length that shows power-law growth with time ξ(t) ∝ t 1/z can be identified in the data and, for large time t, C4(r, t) decays as a power law r −α d with distance r when r ξ(t). The calculation can be interpreted in terms of the maturation metastate averaged Gibbs state, or MMAS, and the decay exponent α d differentiates between a trivial MMAS (α d = 0), as expected in the droplet picture of spin glasses, and a nontrivial MMAS (α d = 0), as in the replica-symmetrybreaking (RSB) or chaotic pairs pictures. We find nonzero α d even in the regime σ > 2/3 which corresponds to short-range systems below six dimensions. For σ < 2/3, the decay exponent α d follows the RSB prediction for the decay exponent αs = 3−4σ of the static metastate, consistent with a conjectured statics-dynamics relation, while it approaches α d = 1 − σ in the regime 2/3 < σ < 1; however, it deviates from both lines in the vicinity of σ = 2/3.

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Section: Simulation Resultsmentioning

confidence: 99%

“…Calculating the exponent α s for low dimension d however remains difficult but there has been recent numerical progress with a Monte Carlo study of the EA model in Ref. [26].…”

Section: Introductionmentioning

confidence: 99%

Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range

Jensen,

Read,

Young

2021

Preprint

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“…The Coulomb potential including gluon loops at next-to-nextto-leading order was evaluated in [49] and extended by fermion loops in Ref. [50]. In the MS scheme, the Coulomb potential reads [51]…”

Section: Sommerfeld Resummationmentioning

confidence: 99%

Squark-pair annihilation into quarks at next-to-leading order

et al. 2019

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The Minimal Supersymmetric Standard Model (MSSM) is under intense scrutiny at the LHC and in dark matter searches. Interestingly, scenarios with light squarks of the third generation remain not only viable, but also well motivated by the observed Standard-Model-like Higgs boson mass and dark matter relic density. The latter often requires important contributions from squark pair annihilation. Following up on previous work, we present in this paper a precision analysis of squark pair annihilation into quarks at next-to-leading order of QCD including Sommerfeld enhancement effects. We discuss all technical details of our one-loop, real emission and resummation calculations, their implementation in the precision tool DM@NLO, as well as the numerical impact on the annihilation cross section and cosmological relic density in phenomenological MSSM scenarios respecting in particular current LHC constraints. We demonstrate that including these radiative corrections leads to substantial shifts in the preferred parameter regions by up to 20 GeV. PACS numbers: 12.38.Bx,12.60.Jv,95.30.Cq,95.35.+d 1 A similar study of the pMSSM has been conducted by the CMS collaboration [28].

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“…An alternative scenario holds that the mean field solution is misleading and the Edwards-Anderson model behaves more like the ferromagnetic Ising model with a simple thermodynamic limit consisting of a single pair of pure states related by a global spin flip. This simpler picture was by developed by McMillan [10], Bray and Moore [11], and Fisher and Huse [12][13][14] [2,15,16] has several strange features, including CSD and support on an uncountable infinity of thermodynamic states. Chuck and Dan also introduced an alternative, perhaps more plausible, scenario also displaying CSD, called the chaotic pairs picture [1].…”

Section: Introductionmentioning

confidence: 99%