1,720,981 research outputs found
Analysis of the planar Ising model beyond the critical Z-invariant setup
No full textDans cette thèse on explore l'existence et l'universalité du modèle d'Ising planaire, dans un cadre critique et presque-critique. En utilisant le formalisme de Kadanoff et Ceva, on étudie grâce à des méthodes d'analyse complexe discrète les limites d'échelles et les propriétés à grandes distance du modèle d'Ising sur les grillesisoradiales ainsi que leur généralisations au modèle d'Ising quantique et aux les s-plongements introduit récemment.In this thesis we explore the existence and the universality of the planar Ising model, at and near criticality. Basing upon the formalism of Kadanoff and Ceva, we study by discrete complex analysis means the scaling limit and large scale properties of the Ising model on isoradial grids, as well as its generalizations to the quantum Ising model and the recently introduced s-embeddings
Ising model and s-embeddings of planar graphs
Full text linkWe discuss the notion of s-embeddings
of planar graphs carrying a nearest-neighbor Ising model. The construction of
is based upon a choice of a global complex-valued
solution of the propagation equation for Kadanoff-Ceva fermions.
Each choice of provides an interpretation of all other fermionic
observables as s-holomorphic functions on . We set up
a general framework for the analysis of such functions on s-embeddings
with . Throughout this analysis, a key role
is played by the functions associated with
, the so-called origami maps in the bipartite dimer model
terminology. In particular, we give an interpretation of the mean curvature of
the limit of discrete surfaces viewed
in the Minkowski space as the mass in the Dirac equation
describing the continuous limit of the model.
We then focus on the simplest situation when have
uniformly bounded lengths/angles and ; as a
particular case this includes all critical Ising models on doubly periodic
graphs via their canonical s-embeddings. In this setup we prove RSW-type
crossing estimates for the random cluster representation of the model and the
convergence of basic fermionic observables. The proof relies upon a new
strategy as compared to the already existing literature, it also provides a
quantitative estimate on the speed of convergence.Comment: 70 pages, 10 figures. Changes in this version: assumption Exp-Fat
clarified, Section 2.7 (discussion of the non-flat setup) extended + minor
changes throughout the tex
Conformal invariance and universality of the dimer model
No full textThis thesis is dedicated to the study of the conformal invariance and the universality of the dimer model on planar bipartite graphs. Kenyon [41, 42] has established the conformal invariance of the limiting distribution of the dimer height function in the case of Temperleyan discretizations, discrete domains on the square lattice with special boundary conditions. In the thesis, we extended Kenyon's result for more general classes of approximations on the square lattice. Yet another direction of research in the dimer model is the universality (which means that the scaling limit is independent of the shape of the lattice) of the planar dimer model. We describe how to construct a circle pattern embedding of a dimer planar graph using its Kasteleyn weights. We also introduce the definition of discrete holomorphicity on such an embedding. We focus on understanding the link between these functions and actual continuous holomorphic functions to study holomorphic observables of the dimer model
Perfect t-embeddings of bipartite planar graphs and the convergence to the GFF -II
No full textWe discuss a concept of `perfect t-embeddingsâ , or `p-embeddings', of weighted bipartite planar graphs. (T-embeddings also appeared under the name Coulomb gauges in a recent work of Kenyon, Lam, Ramassamy and Russkikh.) We believe that these p-embeddings always exist and that they are good candidates to recover the complex structure of big bipartite planar graphs carrying a dimer model. To support this idea, we first develop a relevant theory of discrete holomorphic functions on t-embeddings; this theory unifies Kenyon's holomorphic functions on T-graphs and s-holomorphic functions coming from the Ising model.
Further, given a sequence of (abstract) planar graphs G_n and their p-embeddings T_n onto the unit disc D, assume that (i) the faces of T_n satisfy certain technical assumptions in the bulk of D; (ii) the size of the associated origami maps O_n tends to zero as n grows (again, on each compact subset of D). We prove that (i)+(ii) imply the convergence of the fluctuations of the dimer height functions on G_n (provided that these graphs are embedded by T_n), to the GFF on the unit disc D equipped with the standard complex structure. Though this is not fully clear at the moment, we conjecture that the origami maps O_n are always small in absence of frozen regions and gaseous bubbles, so our theorem can be eventually applied to all such cases.
Moreover, the same techniques are applicable in the situation when the limit of the origami maps arising from a sequence of p-embeddings is a Lorenz-minimal surface, in this situation one eventually obtains the GFF in the conformal parametrization of this surface. In a related joint work with Sanjay Ramassamy we argue that such a Lorenz-minimal surface indeed arises in the case of classical Aztec diamonds; a general conjecture is that this should `always' be the case due to a link between p-embeddings and a representation of the dimer model in the Plucker quadric.
Time permitting, we also indicate how the theory of t-holomorphic functions specifies to the Ising case and discuss related results on conformal invariance of the Ising model as well as a more general perspective.Non UBCUnreviewedAuthor affiliation: ENS-Mitsubishi Heavy IndustriesFacult
Discrete stress energy tensor in the O(n) loop model and the corresponding convergence result for O(1)
No full textNon UBCUnreviewedAuthor affiliation: Steklov InstituteFacult
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
The Inverse Problem for Perturbed Harmonic Oscillator on the Half-Line with a Dirichlet Boundary Condition
Full text linkAbstract.: We consider the perturbed harmonic oscillator in , where is a real-valued potential. We prove that the mapping spectral data = {eigenvalues of T D } {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to is give
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