149 research outputs found
The continuum limit of spin chains
Building on our previous work for and we explore
systematically the continuum limit of gapless vertex models and
spin chains. We find the existence of three possible regimes. Regimes I and II
for are related with Toda, and described by
compact bosons. Regime I for is related with
Toda and involves compact bosons, while regime II is related instead with
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
case. For we find a continuum limit made of
compact and non-compact bosons, while for we find
compact and non-compact bosons. We also find deep relations between
in regime III and the gauged WZW models .Comment: 43 pages, 4 figure
Non compact continuum limit of two coupled Potts models
We study two -state Potts models coupled by the product of their energy
operators, in the regime where the coupling is relevant. A
particular choice of weights on the square lattice is shown to be equivalent to
the integrable 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() 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,
and , 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 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 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 and examine the flow along
the multicritical line between and .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
The "not-A", RSPT and Potts phases in an -invariant chain
We analyse in depth an -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
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