The continuum limit of aN−1(2)a_{N-1}^{(2)} spin chains

Building on our previous work for $a_2^{(2)}$ and $a_3^{(2)}$ we explore systematically the continuum limit of gapless $a_{N-1}^{(2)}$ vertex models and spin chains. We find the existence of three possible regimes. Regimes I and II for $a_{2n-1}^{(2)}$ are related with $a_{2n-1}^{(2)}$ Toda, and described by $n$ compact bosons. Regime I for $a_{2n}^{(2)}$ is related with $a_{2n}^{(2)}$ Toda and involves $n$ compact bosons, while regime II is related instead with $B^{(1)}(0,n)$ super Toda, and involves in addition a single Majorana fermion. The most interesting is regime III, where {\sl non-compact} degrees of freedom appear, generalising the emergence of the Euclidean black hole CFT in the $a_{2}^{(2)}$ case. For $a_{2n}^{(2)}$ we find a continuum limit made of $n$ compact and $n$ non-compact bosons, while for $a_{2n-1}^{(2)}$ we find $n$ compact and $n-1$ non-compact bosons. We also find deep relations between $a_{N-1}^{(2)}$ in regime III and the gauged WZW models $SO(N)/SO(N-1)$.Comment: 43 pages, 4 figure

Non compact continuum limit of two coupled Potts models

We study two $Q$-state Potts models coupled by the product of their energy operators, in the regime $2 < Q \le 4$ where the coupling is relevant. A particular choice of weights on the square lattice is shown to be equivalent to the integrable $a_3^{(2)}$ vertex model. It corresponds to a selfdual system of two antiferromagnetic Potts models, coupled ferromagnetically. We derive the Bethe Ansatz equations and study them numerically for two arbitrary twist angles. The continuum limit is shown to involve two compact bosons and one non compact boson, with discrete states emerging from the continuum at appropriate twists. The non compact boson entails strong logarithmic corrections to the finite-size behaviour of the scaling levels, the understanding of which allows us to correct an earlier proposal for some of the critical exponents. In particular, we infer the full set of magnetic scaling dimensions (watermelon operators) of the Potts model.Comment: 33 pages, 10 figures v2: reference added, minor typo corrected v3: revised version for publication in JSTAT: section 3.1 added, some technical content moved to appendi

A new look at the collapse of two-dimensional polymers

We study the collapse of two-dimensional polymers, via an O($n$) model on the square lattice that allows for dilution, bending rigidity and short-range monomer attractions. This model contains two candidates for the theta point, $\Theta_{\rm BN}$ and $\Theta_{\rm DS}$, both exactly solvable. The relative stability of these points, and the question of which one describes the `generic' theta point, have been the source of a long-standing debate. Moreover, the analytically predicted exponents of $\Theta_{\rm BN}$ have never been convincingly observed in numerical simulations. In the present paper, we shed a new light on this confusing situation. We show in particular that the continuum limit of $\Theta_{\rm BN}$ is an unusual conformal field theory, made in fact of a simple dense polymer decorated with {\sl non-compact degrees of freedom}. This implies in particular that the critical exponents take continuous rather than discrete values, and that corrections to scaling lead to an unusual integral form. Furthermore, discrete states may emerge from the continuum, but the latter are only normalizable---and hence observable---for appropriate values of the model's parameters. We check these findings numerically. We also probe the non-compact degrees of freedom in various ways, and establish that they are related to fluctuations of the density of monomers. Finally, we construct a field theoretic model of the vicinity of $\Theta_{\rm BN}$ and examine the flow along the multicritical line between $\Theta_{\rm BN}$ and $\Theta_{\rm DS}$.Comment: v2 : references adde

Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III

The so-called regime III of the a_2^{(2)} Izergin-Korepin 19-vertex model has defied understanding for many years. We show in this paper that its continuum limit involves in fact a non compact conformal field theory (the so-called Witten Euclidian black hole CFT), which leads to a continuous spectrum of critical exponents, as well as very strong corrections to scaling. Detailed numerical evidence based on the Bethe ansatz analysis is presented, involving in particular the observation of discrete states in the spectrum, in full agreement with the string theory prediction for the black hole CFT. Our results have important consequences for the physics of the O(n) model, which will be discussed elsewhere.Comment: 57 pages, 19 figures; v2: reference adde

Impacts sociaux, économiques et politiques du blanchiment de capitaux (Social, economic and political impacts of money laundering)

Le blanchiment de capitaux provoque dans les économies des dégâts considérables. Il est néanmoins nécessaire d’éviter le manichéisme angélique qui consiste à dire que «la guerre, c’est pas beau». En effet, certains pays et certains peuples profitent de la manne financière issue du blanchiment. Cet article s’évertue donc à montrer plusieurs facettes de l’impact du blanchiment de capitaux sur les économies, qu’elles soient positives ou négatives. Il montre qu’une volonté évidente de lutter contre ce fléau doit être nuancée par des considérations sociales et politiques. Money laundering causes important damages in economy. Nevertheless, we should stop playing the innocent: some countries do take advantage from the financial sources that money laundering enables. This article aims at distinguishing the different impacts that money laundering has on economy, impact that could be either positive or negative. In spite of evident urge to fight against this curse, we discuss the fact that opinions should be more finely-shadedmany laundering, finance, globalization

Symmetry-breaking-induced loss of ergodicity in maps of the simplex with inversion symmetry

Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of the simplex with arbitrary number of vertices - that exhibit several asymmetric absolutely continuous invariant measures when their expanding rate is sufficiently small. In a preliminary study, we consider arbitrary maps of the multi-dimensional torus with permutation symmetries. Using these symmetries, we show that the existence of multiple invariant sets of such maps can be obtained from their analogues in some reduced maps of a smaller phase space. For the coupled maps, this reduction yields inversion-symmetric maps of the simplex. The subsequent analysis of these reduced maps show that their systematic dynamics is intractable because some essential features vary with the number of units; hence the substitutes which nonetheless capture the coupled maps common characteristics. The construction itself is based on a simple mechanism for the generation of asymmetric invariant union of polytopes, whose basic principles should extend to a broad range of maps with permutation and inversion symmetries

La banalisation du luxe (Democratization of luxury) Abstract : La plupart des achats pratiqués sont effectués par des clients occasionnels, ce qui a conduit les entreprises à s’adapter par une nouvelle stratégie. En effet, suite à l’intensification de la concurrence et à la concentration du secteur qui engendrent une contrainte de rentabilité immédiate, mais aussi en raison des impératifs nouveaux du marché, les maisons de luxe se voient obligées d’élargir leur offre afin d’ajouter à une clientèle dite traditionnelle une clientèle plus vaste. Dès lors, le secteur du luxe est progressivement passé d’une logique d’offre où seul un nombre restreint de personnes était ciblé, à une politique d’offre où des professionnels du marketing étudient la demande du marché afin d’orienter la production des biens vers un marché de masse. La banalisation est une problématique capitale et décisive car les maisons de luxe doivent préserver leur image de marque tout en élargissant leur clientèle : elles s’efforcent de créer et de pérenniser leurs marques, sans jamais oublier qu’une marque ne peut pas s’associer à n’importe quel objet, sous peine de menacer l’ensemble de ses représentations. Par conséquent, chaque nouveau produit présente un risque pour la gamme toute entière, d’où le risque d’une erreur stratégique par le choix de la banalisation. Le danger est de voir la clientèle aisée se tourner vers d’autres grands noms pratiquant toujours cet esprit d’élitisme qui caractérise le « luxe ». The luxury market is no longer reserved for an elite as its evolution over the last fifteen years clearly indicates. Luxury goods companies have been forced to adapt and resort to new strategies to take into account the fact that most purchases are now made by occasional clients. The keen competition and the on-going concentration in that sector – with the resulting short term profitability constraints - together with the new market conditions, have forced luxury goods companies to broaden their offer so as to add new customers to their traditional base. As a consequence, the luxury market has progressively moved away from an offer-driven logic – targeting a small number of people – in favor of an offer-based policy with marketing professionals studying market demand so as to direct the production of goods towards mass production. The democratization of luxury constitutes a major challenge for those companies which must preserve their image while broadening their customer base: they now strive to create and perpetuate their brand image, without ever forgetting that a brand cannot be associated to just any object, as this might constitute a threat to all its brand representations. Thus every new product constitutes a real threat to the whole range and there is a risk of making a strategic mistake by appealing to the mass market; and there is also a clear danger of seeing affluent customers turn to other great names that still foster this ‘elite spirit’ that characterizes « luxury ».

democratization, luxury, marketing

The "not-A", RSPT and Potts phases in an S3S_3-invariant chain

We analyse in depth an $S_3$-invariant nearest-neighbor quantum chain in the region of a U(1)-invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Also nearby is a phase with "representation" symmetry-protected topological (RSPT) order. Its dual exhibits an unusual "not-A" order, where the spins prefer to align in two of the three directions. Within each of the four phases, we find a frustration-free point with exact ground state(s). The exact RSPT ground state is similar to that of Affleck-Kennedy-Lieb-Tasaki, whereas its dual states in the not-A phase are product states, each an equal-amplitude sum over all states where one of the three spin states on each site is absent. A field-theory analysis shows that all transitions are in the universality class of the critical three-state Potts model. They provide a lattice realization of a flow from a free-boson field theory to the Potts conformal field theory.Comment: 14 pages, 5 figures. v2: refined the SPT discussion, and added one letter to the title. v3: further refinement, n.b. RSPT in title is spelled out in journa

Impact des résultats passés sur l’aversion au risque de l’investisseur (The impact of past results on the investor's risk).

Dans un contexte de crise, il est facile de perdre ses repères, et les comportements irrationnels actuels, la panique généralisée des investisseurs le démontrent. Alors que de nombreuses cessations de paiement des ménages américains étaient constatées depuis plusieurs mois, de nombreux investisseurs ont continué à acheter des produits liés au marché des subprimes. Une lecture de l’histoire financière souligne le caractère récurrent et global des anomalies de marché. Le présent article cherche à savoir en quoi de bons résultats financiers passés influencent l’aversion au risque d’un investisseur. In a context of crisis, it is easy to lose its points of reference; the current irrational behaviours and the general panic of investors demonstrate it. While for sevenal months, many american households have been unable to meet their financial obligation, some investors have kept on buying financial products linked to the market of the subprimes. An interpretation of the financial history underlines the recurring and global character of the markets' abnormalities. The present article tries to know how good financial results achieved in the past can influence the investor’s risk aversion.irrational behaviors, financial history, investor’s risk aversion

Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results

We address the computation of the Loschmidt echo in interacting integrable spin chains after a quantum quench. We focus on the massless regime of the XXZ spin-1/2 chain and present exact results for the dynamical free energy (Loschmidt echo per site) for a special class of integrable initial states. For the first time we are able to observe and describe points of non-analyticities using exact methods, by following the Loschmidt echo up to large real times. The dynamical free energy is computed as the leading eigenvalue of an appropriate Quantum Transfer Matrix, and the non-analyticities arise from the level crossings of this matrix. Our exact results are expressed in terms of \u201cexcited-state\u201d thermodynamic Bethe ansatz equations, whose solutions involve non-trivial Riemann surfaces. By evaluating our formulas, we provide explicit numerical results for the quench from the N\ue9el state, and we determine the first few non-analytic points. \ua9 2018 The Author(s