Lifted worm algorithm for the Ising model

Elçi, Eren Metin; Grimm, Jens; Ding, Lijie; Nasrawi, Abrahim; Garoni, Timothy M.; Deng, Youjin

doi:10.1103/physreve.97.042126

Cited by 15 publications

(9 citation statements)

References 33 publications

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“…For the critical 4D SAW, in comparison with the Metropolis algorithm, the efficiency is improved by more than 100 times [11]. For the complete graph, the irreversible BS algorithm is qualitatively more efficient than the reversible methods, as for the irreversible worm algorithm [48].…”

Section: Observables and Fss Analysis A Model And Algorithmmentioning

confidence: 99%

Logarithmic finite-size scaling of the self-avoiding walk at four dimensions

Fang,

Deng,

Zhou

2021

Preprint

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The n-vector spin model, which includes the self-avoiding walk (SAW) as a special case for the n → 0 limit, has an upper critical dimensionality at four spatial dimensions (4D). We simulate the SAW on 4D hypercubic lattices with periodic boundary conditions (PBCs) by an irreversible Berretti-Sokal algorithm up to linear size L = 768. From an unwrapped end-to-end distance, we obtain the critical fugacity as zc = 0.147 622 380(2), improving over the existing result zc = 0.147 622 3(1) by 50 times. Such a precisely estimated critical point enables us to perform a systematic study of the finite-size scaling of 4D SAW for various quantities. Our data indicate that near zc, the scaling behavior of the free energy simultaneously contains a scaling term from the Gaussian fixed point and the other accounting for multiplicative logarithmic corrections. In particular, it is clearly observed that the critical magnetic susceptibility and the specific heat logarithmically diverge as χ ∼ L 2 (ln L) 2ŷ h and C ∼ (ln L) 2ŷt , and the logarithmic exponents are determined as ŷh = 0.252(2) and ŷt = 0.25(2), in excellent agreement with the field theoretical prediction ŷh = ŷt = 1/4. Our results provide a strong support for the recently conjectured finite-size scaling form for the O(n) universality classes at 4D.

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Section: Observables and Fss Analysis A Model And Algorithmmentioning

confidence: 99%

Logarithmic finite-size scaling of the self-avoiding walk at four dimensions

Fang,

Deng,

Zhou

2021

Preprint

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“…This algorithm was used due to its implementational simplicity, rather than its efficiency, and we note that more sophisticated Markov chain Monte Carlo algorithms are available (e.g. Elçi et al, 2018).…”

Section: E1 Conway-maxwell-poisson Modelmentioning

confidence: 99%

Generalised Bayesian Inference for Discrete Intractable Likelihood

Matsubara¹,

Knoblauch²,

Briol³

et al. 2022

Preprint

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Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper addresses this computational challenge through the development of a novel generalised Bayesian inference procedure suitable for discrete intractable likelihood. Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood. The result is a generalised posterior that can be sampled using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalising constant. The statistical properties of the generalised posterior are analysed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalised posteriors is proposed. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalised Bayesian inference at low computational cost.theoretical guarantees, and can be computed in a cost O(nd) that is linear in the size of the dataset. Full details of the DFD-Bayes approach are provided next. MethodologyThis section presents and analyses DFD-Bayes. First, we present a novel discrete formulation of the Fisher divergence in Section 3.1. DFD-Bayes is introduced in Section 3.2, where posterior consistency and a Bernstein-von Mises result are established. Section 3.3 presents a novel approach to calibration of generalised posteriors, which may be of independent interest. Limitations of DFD-Bayes are discussed in Section 3.4.Notation Denote by X a countable set in which data are contained, and by Θ the set of permitted values for the parameter θ, where Θ is a Borel subset of R p for some p ∈ N. Probability distributions on X are identified with their probability mass functions, with respect to the counting measure on X . The i-th coordinate of a function f : X → R m is denoted by f i : X → R. For a probability distribution q on X and m, p ∈ N, denote by L p (q, R m ) the vector space of measurable functions f : X → R m such that m i=1 E X∼q [f i (X) p ] < ∞. For z ∈ R m , the Euclidean norm is denoted z . A Dirac measure at x ∈ X is denoted by δ x .

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“…The former expands the Boltzmann factor of each bond to decouple spins, which can be generalized to higher dimensions; The latter keeps track of the domain-wall boundaries on the dual lattice. The CP configurations in the two expansions can be sampled by the worm algorithm [26][27][28][29][30], which is at least as efficient as cluster algorithms for the spin representation. Moreover, it is very convenient to measure the two-point correlation function in the worm simulation.…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo study of the duality and BKT phase transitions of the two-dimensional $q$-state clock model in flow representations

Chen¹,

Hou²,

Fang³

et al. 2022

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The two-dimensional (2D) q-state clock model for q ≥ 5 undergoes two Berenzinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive wormtype simulation of the square-lattice clock model for q = 5 to 9 in a pair of flow representations, respectively from the high-and low-temperature expansions. By finite-size scaling analysis of susceptibility-like quantities, we determine the critical points with a precision improving over the existing results. Thanks to the dual flow representations, each point in the critical region is observed to simultaneously exhibit a pair of anomalous dimensions, which are (η1 = 1/4, η2 = 4/q 2 ) at the two BKT transitions. Further, the approximate self-dual points β sd (L), defined by the stringent condition that the susceptibility-like quantities in both flow representations are identical, are found to be nearly independent of system size L and behave as β sd q/2π asymptotically at the large-q limit. The exponent η at β sd is consistent with 1/q within statistical errors as long as q ≥ 5. Our work provides a vivid demonstration of rich phenomena associated with the duality and self-duality of the clock model in two dimensions.

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Lifted worm algorithm for the Ising model

Cited by 15 publications

References 33 publications

Logarithmic finite-size scaling of the self-avoiding walk at four dimensions

Logarithmic finite-size scaling of the self-avoiding walk at four dimensions

Generalised Bayesian Inference for Discrete Intractable Likelihood

A Monte Carlo study of the duality and BKT phase transitions of the two-dimensional $q$-state clock model in flow representations

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