Bootstrap, Markov Chain Monte Carlo, and LP/SDP hierarchy for the lattice Ising model

IF 5 1区物理与天体物理 Q1 PHYSICS, PARTICLES & FIELDS

Journal of High Energy Physics Pub Date : 2023-11-09 DOI:10.1007/jhep11(2023)047

Minjae Cho, Xin Sun

引用次数: 1

Abstract

A bstract Bootstrap is an idea that imposing consistency conditions on a physical system may lead to rigorous and nontrivial statements about its physical observables. In this work, we discuss the bootstrap problem for the invariant measure of the stochastic Ising model defined as a Markov chain where probability bounds and invariance equations are imposed. It is described by a linear programming (LP) hierarchy whose asymptotic convergence is shown by explicitly constructing the invariant measure from the convergent sequence of moments. We also discuss the relation between the LP hierarchy for the invariant measure and a recently introduced semidefinite programming (SDP) hierarchy for the Gibbs measure of the statistical Ising model based on reflection positivity and spin-flip equations.

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自举，马尔科夫链蒙特卡罗，和LP/SDP层次的晶格Ising模型

抽象引导是一种思想，它认为在物理系统上施加一致性条件可能会导致关于其物理可观察对象的严格和非平凡的陈述。在这项工作中，我们讨论了定义为马尔可夫链的随机Ising模型的不变量测度的自举问题，该模型具有概率界和不变量方程。用线性规划(LP)层次来描述它的渐近收敛性，该层次通过从收敛的矩序列显式构造不变测度来证明。我们还讨论了基于反射正性和自旋翻转方程的统计Ising模型的不变测度的LP层次与最近引入的吉布斯测度的半定规划(SDP)层次之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of High Energy Physics PHYSICS, PARTICLES & FIELDS-

CiteScore

10.00

自引率

46.30%

发文量

2107

审稿时长

12 weeks

期刊介绍： The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).