The Coleman correspondence at the free fermion point

Bauerschmidt, Roland; Webb, Christian A.

doi:10.48550/arxiv.2010.07096

Cited by 4 publications

(5 citation statements)

References 41 publications

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“…Indeed, the two-point function of the gradient of the discrete GFF is known to decay like the inverse square of the distance (see e.g. [6]).…”

Section: 5mentioning

confidence: 99%

Spins, percolation and height functions

Lis

2022

Electron. J. Probab.

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To highlight certain similarities in graphical representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning of the parameters.To be precise, our model consists of two independent standard Potts models, with possibly different numbers of spins and different coupling constants (the four parameters of the model), defined jointly on a graph embedded in a surface and its dual graph, and conditioned on the event that the primal and dual interfaces between spins of different value do not intersect. We also introduce naturally coupled height function and bond percolation models, and we discuss fundamental properties of the resulting joint coupling.As special cases we recover the standard Potts and random cluster model, the six-vertex model and loop O(n) model, the random current, double random current and XOR-Ising model.

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“…Indeed, the two-point function of the gradient of the discrete GFF is known to decay like the inverse square of the distance (see e.g. [6]).…”

Section: 5mentioning

confidence: 99%

Spins, percolation and height functions

Lis

2022

Electron. J. Probab.

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“…(E.g., see [4, Section 2.7] for a relevant discussion under the additional assumption ϑ ∈ R specific to the Ising model setup.) In the theoretical physics language, in this setup the limit of height fluctuations should be described by the bosonization of free massive fermions, which leads to the sine-Gordon theory with a special value of the interaction parameter rather than to free bosons; e.g., see [1] and references therein. Coming back to the dimer model language, this means that we do not expect the height fluctuations to have a Gaussian structure in the small mesh size limit if m(ζ) = 0; cf.…”

Section: [±±]mentioning

confidence: 99%

Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces

Chelkak¹,

Laslier²,

Russkikh³

2021

Preprint

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This is the second paper in the series devoted to the study of the dimer model on t-embeddings of planar bipartite graphs. We introduce the notion of perfect t-embeddings and assume that the graphs of the associated origami maps converge to a Lorentz-minimal surface S ξ as δ → 0. In this setup we prove (under very mild technical assumptions) that the gradients of the height correlation functions converge to those of the Gaussian Free Field defined in the intrinsic metric of the surface S ξ . We also formulate several open questions motivated by our work.

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“…Remarkably, many of the models listed here have non-Gaussian or non-determinantal infrared fixed points, and results are robust under a large class of microscopic perturbations of the lattice Hamiltonian. Moreover, this approach led to the proof of several predictions from CFT, such as scaling relations among critical exponents and amplitudes [10,28], bosonization identities [5,7], and expression for the universal subleading contributions to the critical free energy [24]. A limitation of this approach is that it is restricted to 'weakly interacting' cases, that is, to models that are close to a Gaussian model or to a free Fermi model.…”

Section: Introductionmentioning

confidence: 99%

Conformal invariance and Renormalization Group

Giuliani¹

2020

Preprint

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Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a quantum critical point. Conformal invariance is expected to be a feature of the fixed point theory obtained from a microscopic model at criticality, under appropriate averaging and rescaling operations: the action of the Wilsonian Renormalization Group (RG). Unfortunately, an explicit connection between critical microscopic models and their conformally invariant scaling limit is still lacking in general. Nevertheless, the last decades witnessed significant progress on this topic, both from the mathematical and physics sides, where several new tools have been introduced and their ranges of applications have constantly and significantly increased: I refer here, e.g., to discrete holomorphicity, SLE, the use of lattice Ward Identities in constructive RG, the conformal bootstrap program and its recent applications to 3D CFT. In an effort to make further progress on these problems, the one-day workshop Emergent CFTs in statistical mechanics was organized and held at Institut Curie in Paris on January 29, 2020: the goal was to bring together probabilists, mathematical physicists and theoretical physicists, working on various aspects of critical statistical mechanics systems with complementary tools, both at the discrete and the continuum level, in the hope of creating new connections between the different approaches. This paper is based on an introductory talk given at the workshop: after a summary of the main topics discussed in the meeting, I illustrate the approach to the problem based on constructive RG methods, by reviewing recent results on the existence and the explicit characterization of the scaling limit of critical 2D Ising models with finite range interactions in cylindrical geometry.

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The Coleman correspondence at the free fermion point

Cited by 4 publications

References 41 publications

Spins, percolation and height functions

Spins, percolation and height functions

Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces

Conformal invariance and Renormalization Group

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