1,720,978 research outputs found
Critical behavior of Ising spin systems: Phase transition, metastability and ergodicity
No full textPhysical phenomena commonly observed in nature such as phase transitions, critical phenomena and metastability when studied froma mathematical point of view may give arise to a rich variety of behavior whose study becomes interesting in itself. In Chapter 1 we illustrate the phase transition phenomenon at low temperatures for one-dimensional long range Ising models with inhomogeneous external fields. More precisely, we consider Ising spins arranged on the one-dimensional integer lattice where such spins interact via ferromagnetic pairwise interactions whose strength is inversely proportional to their distance to the power ®; furthermore, the system is put under the influence of an external magnetic field that vanishes with polynomial power ± as the distance between the spin and the origin increases. In that case we show that a phase transition manifests itself in the form of the existence of two distinct infinite-volume Gibbs states, obtained by means of the application of the thermodynamic limit considering “plus” and “minus” boundary conditions respectively, whenever the system is subject at low temperatures and an inequality involving ® and ± holds. The proof of this result is done by means of the Peierls’ contour argument adapted to one-dimensional long range Ising models, first introduced by J. Fröhlich and T. Spencer in 1982 and later modified by M. Cassandro, P.A. Ferrari, I. Merola and E. Presutti in 2005. Our results improve the one obtained by the latter authors since we managed to avoid the assumption of large nearest-neighbor interactions and added the influence of an external field, showing an interplay between the constants ® and ± in order to guarantee the manifestation of the phase transition.Applied Probabilit
Bosonic and fermionic structures in lattice models
No full textWe study the behavior of gradients squared of Gaussian fields on different graphs and their relationship with certain lattice models. In particular, we study commutative and anti-commutative squared Gaussian fields, and used them to calculate correlation functions of lattice models like the Abelian sandpile model (ASM) and uniform spanning tree (UST).
The first model to be studied is the gradient squared of the bosonic discrete Gaussian free field (dGFF) on Z^d. We first prove that this field converges to white noise in the thermodynamic limit. We also calculate its joint moments explicitly, which unveil a quasi permanental structure. We observe a similarity with the height-one field of the ASM. This is a lattice model in which every vertex on a finite grid has a value corresponding to the slope of a pile. This slope gradually increases as “grains of sand” are randomly added to the grid. When the slope surpasses a threshold the site collapses, redistributing sand to adjacent sites. When depositing grains of sand randomly, each deposition might trigger a chain reaction, impacting multiple sites. Once the system attains stationarity, we can define the height-one field as the indicator function of each site having 1 grain. In Dürre (Stoch. Process. Appl. 119(9):2725–2743, 2009) the author studies its joint cumulants in the limit, which are uncannily similar to the ones we obtained for our field, albeit with an sign of difference, having a quasi determinantal structure, instead of permanental. This similarity then begs the question: What modification of this field produces the same moments as the height-one field of the ASM?
Here is where the Grassmannian or fermionic variables come into play. If we replace the Gaussian variables by fermionic Gaussians we obtain the exact same moments expression as Dürre. What is more, our calculation method allows us to generalize the proof to any dimension, and to the triangular and hexagonal lattices in 2d, hinting towards a potential universality property. It has been conjectured that the ASM in the limit should correspond to a logarithmic CFT, an example of which is the field theory whose action is given by the gradient squared of a free fermion. We believe that our joint moments correspondence hints in that direction.
This equality poses a new question: Why? What does the fermionic GFF have to do with the ASM, so that our particular function yields the same moments as the height-one field? It is well-known that the height-one field configurations can be put in one-to-one correspondence with UST realizations. It is also known that there is a connection between UST configurations and fermionic variables. In particular, the probabilities of some edges belonging to the UST can be calculated as determinants of specific matrices, which can be expressed as expectations of products of fermionic variables. We also extend those techniques in order to find closed-form expressions of the PMF of the degree field of the UST in these lattices. To the author’s knowledge, this is the first time such expressions are given in the literature
Motional narrowing in the time-averaging approximation for simulating two-dimensional nonlinear infrared spectra
No full textThe diagonal linewidth in two-dimensional infrared spectra is often narrower than the distribution of transition frequencies. The width along the antidiagonal is broader than predicted by the lifetime broadening. These effects arise from time-dependent fluctuations of the transition frequencies. They can be accounted for with a semiclassical approach. For systems with many coupled vibrational modes, this approach, however, becomes computationally too demanding to be practically applicable. A time-averaging approximation was suggested for linear infrared absorption spectra. In this paper, we demonstrate that the averaging can be optimized to fit a broader scale of frequency fluctuations by using a Gaussian weight function instead of the originally proposed box function. We further generalize the time-averaging method to allow the simulation of two-dimensional infrared spectra and demonstrate the method on a simple system. The approximation delivers a large speed-up of the calculation without losing significant accuracy
Mean-field avalanche size exponent for sandpiles on Galton–Watson trees
No full textWe show that in Abelian sandpiles on infinite Galton–Watson trees, the probability that the total avalanche has more than t topplings decays as t- 1 / 2. We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (Probab Theory Relat Fields 125:259–265, 2003), that was previously used by Lyons et al. (Electron J Probab 13(58):1702–1725, 2008) to study uniform spanning forests on Zd, d≥ 3 , and other transient graphs.Applied Probabilit
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
Scaling Limits in Divisible Sandpiles: A Fourier Multiplier Approach
No full textIn this paper we investigate scaling limits of the odometer in divisible sandpiles on d-dimensional tori following up the works of Chiarini et al. (Odometer of long-range sandpiles in the torus: mean behaviour and scaling limits, 2018), Cipriani et al. (Probab Theory Relat Fields 172:829–868, 2017; Stoch Process Appl 128(9):3054–3081, 2018). Relaxing the assumption of independence of the weights of the divisible sandpile, we generate generalized Gaussian fields in the limit by specifying the Fourier multiplier of their covariance kernel. In particular, using a Fourier multiplier approach, we can recover fractional Gaussian fields of the form (- Δ) - s / 2W for s> 2 and W a spatial white noise on the d-dimensional unit torus.Applied Probabilit
Self-avoiding pruning random walk on signed network
No full textA signed network represents how a set of nodes are connected by two logically contradictory types of links: positive and negative links. In a signed products network, two products can be complementary (purchased together) or substitutable (purchased instead of each other). Such contradictory types of links may play dramatically different roles in the spreading process of information, opinion, behaviour etc. In this work, we propose a self-avoiding pruning (SAP) random walk on a signed network to model e.g. a user's purchase activity on a signed products network. A SAP walk starts at a random node. At each step, the walker moves to a positive neighbour that is randomly selected, the previously visited node is removed and each of its negative neighbours are removed independently with a pruning probability r. We explored both analytically and numerically how signed network topological features influence the key performance of a SAP walk: the evolution of the pruned network resulted from the node removals, the length of a SAP walk and the visiting probability of each node. These findings in signed network models are further verified in two real-world signed networks. Our findings may inspire the design of recommender systems regarding how recommendations and competitions may influence consumers' purchases and products' popularity.Multimedia ComputingApplied Probabilit
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
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