Toward a 3d Ising model with a weakly-coupled string theory dual

Iqbal, Nabil; McGreevy, John

doi:10.21468/scipostphys.9.2.019

Cited by 23 publications

(21 citation statements)

References 61 publications

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“…(Of course it is strongly coupled even in its particle description). This is entirely consistent with previous attempts at describing the 3d Ising model as a string theory, where it appears that a large string coupling g s is an unavoidable feature of the description [21,57].…”

Section: Lack Of Universalitysupporting

confidence: 91%

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

Iqbal¹,

McGreevy²

2021

Preprint

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By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field -defined on the space of closed loops -that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

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Section: Lack Of Universalitysupporting

confidence: 91%

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

Iqbal¹,

McGreevy²

2021

Preprint

Self Cite

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“…As in two dimensions, we expect the Fisher metric to diverge at the critical point determined numerically, for instance in [58], or using the conformal bootstrap as in [59]. The Fisher metric approach may also be of relevance for interpreting the 3d Ising model as a string theory, as proposed by Polyakov [60] and recently considered by Iqbal and McGreevy [61]. Here, the domain walls that separate up from down spins are interpreted as string worldsheets.…”

Section: Discussionmentioning

confidence: 91%

“…Here, the domain walls that separate up from down spins are interpreted as string worldsheets. As argued in [61], the identification of the world sheet target space with AdS 4 does not lead to a conformally invariant worldsheet sigma model. We expect that an interesting avenue to proceed in this context is to the determine the probability distribution of the domain wall worldsheet sigma model and to calculate the associated Fisher metric.…”

Section: Discussionmentioning

confidence: 96%

Information geometry in quantum field theory: lessons from simple examples

2020

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Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By studying their Fisher metrics, we derive some general lessons that may have important implications for the application of information geometry in holography. We begin by demonstrating that the symmetries of the physical theory under study play a strong role in the resulting geometry, and that the appearance of an AdS metric is a relatively general feature. We then investigate what information the Fisher metric retains about the physics of the underlying theory by studying the geometry for both the classical 2d Ising model and the corresponding 1d free fermion theory, and find that the curvature diverges precisely at the phase transition on both sides. We discuss the differences that result from placing a metric on the space of theories vs.~states, using the example of coherent free fermion states. We compare the latter to the metric on the space of coherent free boson states and show that in both cases the metric is determined by the symmetries of the corresponding density matrix. We also clarify some misconceptions in the literature pertaining to different notions of flatness associated to metric and non-metric connections, with implications for how one interprets the curvature of the geometry. Our results indicate that in general, caution is needed when connecting the AdS geometry arising from certain models with the AdS/CFT correspondence, and seek to provide a useful collection of guidelines for future progress in this exciting area.

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“…The Ising model thus comprises a particular universality class [7], which describes the grouping of many different systems according to some key common features in their phase transitions [8]. The Ising model has been used for diverse purposes, from describing the liquid-gas critical point to representing various features of string theory [9][10][11][12]. This is remarkable for such a simple model.…”

Section: Introductionmentioning

confidence: 99%

Magnetisation and Mean Field Theory in the Ising Model

Sakthivadivel

2022

SciPost Phys. Lect. Notes

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In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

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Toward a 3d Ising model with a weakly-coupled string theory dual

Cited by 23 publications

References 61 publications

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

Information geometry in quantum field theory: lessons from simple examples

Magnetisation and Mean Field Theory in the Ising Model

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