Convergent perturbation theory for lattice models with fermions

Sazonov, Vasily

doi:10.1142/s0217751x1650072x

Cited by 9 publications

(3 citation statements)

References 21 publications

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“…The presented construction can be generalized to the fermionic lattice models by employing bosonization. For instance, an application of the method [9][10][11][12][13] to the bosonized fermionic model, a model of lattice QED, was proposed in [38]. The problem of the bosonizations of the complex actions has been recently solved in [39].…”

Section: Discussionmentioning

confidence: 99%

Convergent series for lattice models with polynomial interactions

Ivanov

Sazonov

2017

Nuclear Physics B

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The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of the perturbative expansions by a certain interacting model or regularizing original lattice integrals, one can construct desired convergent series. In this paper we develop methods, which are based on the joint and separate utilization of the regularization and new initial approximation. We prove, that the convergent series exist and can be expressed as the re-summed standard perturbation theory for any model on the finite lattice with the polynomial interaction of even degree. We discuss properties of such series and make them applicable to practical computations. The workability of the methods is demonstrated on the example of the lattice $\phi^4$-model. We calculate the operator $\langle\phi_n^2\rangle$ using the convergent series, the comparison of the results with the Borel re-summation and Monte Carlo simulations shows a good agreement between all these methods.Comment: 25 pages, 14 figure

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Section: Discussionmentioning

confidence: 99%

Convergent series for lattice models with polynomial interactions

Ivanov

Sazonov

2017

Nuclear Physics B

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“…Кроме того, он позволяет задумываться о решении принципиально новых задач, таких как, например, исследование асимптотик сильной связи. Очевидные с математической точки зрения (сходимость ряда теории возмущений) преимущества данного подхода инициировали попытки его расширения на более общий класс рассматриваемых моделей [9], [10]. К сожалению, в упомянутых выше работах авторы для оценки радиусов сходимости получаемых рядов пользуются, вслед за оригинальной работой [6], неравенствами Соболева вместо более точного анализа, предложенного позднее в работах [7], [8].…”

Section: Introductionunclassified

Convergent perturbation theory for studying phase transitions

Налимов¹,

Nalimov

Овсянников³

et al. 2020

TMF

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Предложен метод построения теории возмущений с конечным радиусом сходимости для достаточно широкого класса квантово-полевых моделей, традиционно применяемых к описанию критического и околокритического поведения в задачах статистической физики. Для предлагаемых сходящихся рядов при помощи инстантонного анализа определен радиус сходимости, а также указан способ вычисления их коэффициентов, опирающийся на диаграммы стандартной (расходящейся) теории возмущений. Подход апробирован на примере стандартной $\mathrm A$-модели стохастической динамики и матричной модели фазового перехода в системе нерелятивистских фермионов, в которой его применение позволило объяснить ранее обнаруженное квазиуниверсальное поведение траекторий фазового перехода первого рода.

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“…Nevertheless, considering a suitable regularization of the path or lattice integrals [3,4,5,6,7,8,9] or changing the initial Gaussian approximation to an appropriate interacting theory [10,11] one can construct convergent series (CS). Recently, the applications of the convergent series methods to a model of lattice QED [12] and to the continuous Yang-Mills and QCD [13] were proposed. This gives a strong motivation for the detailed studies of the CS.…”

Section: Introductionmentioning

confidence: 99%

Convergent Perturbation Theory for the lattice $\phi^4$-model

Ivanov¹,

Sazonov²,

Belokurov³

et al. 2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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The standard lattice perturbation theory leads to the asymptotic series because of the incorrect interchange of the summation and integration. However, changing the initial approximation of the perturbation theory, one can generate the convergent series. We study the lattice ϕ 4-model and compare the operator ⟨ϕ 2 n ⟩ calculated using the convergent series and obtained by Monte Carlo simulations.

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Convergent perturbation theory for lattice models with fermions

Cited by 9 publications

References 21 publications

Convergent series for lattice models with polynomial interactions

Convergent series for lattice models with polynomial interactions

Convergent perturbation theory for studying phase transitions

Convergent Perturbation Theory for the lattice $\phi^4$-model

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