Algebraic arctic curves in the domain-wall six-vertex model

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte

Emptiness and Depletion Formation Probability in spin models with inverse square interaction

We calculate the Emptiness Formation Probability (EFP) in the spin-Calogero Model (sCM) and Haldane-Shastry Model (HSM) using their hydrodynamic description. The EFP is the probability that a region of space is completely void of particles in the ground state of a quantum many body system. We calculate this probability in an instanton approach, by considering the more general problem of an arbitrary depletion of particles (DFP). In the limit of large size of depletion region the probability is dominated by a classical configuration in imaginary time that satisfies a set of boundary conditions and the action calculated on such solution gives the EFP/DFP with exponential accuracy. We show that the calculation for sCM can be elegantly performed by representing the gradientless hydrodynamics of spin particles as a sum of two spin-less Calogero collective field theories in auxiliary variables. Interestingly, the result we find for the EFP can be casted in a form reminiscing of spin-charge separation, which should be violated for a non-linear effect such as this. We also highlight the connections between sCM, HSM and $\lambda=2$ spin-less Calogero model from a EFP/DFP perspective.Comment: 26 pages, no figure

On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions

The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation function can be used as building block for computing various (both local and nonlocal) correlation functions in the model. The row configuration probability is calculated using the quantum inverse scattering method; the final result is given in terms of a multiple integral. The connection with the emptiness formation probability, another nonlocal correlation function which was computed elsewhere using similar methods, is also discussed.Comment: 15 pages, 2 figure

EU competition law in the regulated network industries

This piece considers the interface between EU competition law and the regulation of network industries. The two have been transformed as a result of their interactions. It is difficult to make sense of contemporary EU competition law without taking into account the consequences that the liberalisation process has had on it. Similarly, regulation sees EU competition law as a model and an aspiration. In this sense, the two disciplines can be said to be mutually compatible. In spite of the compatibility between EU competition law and sector-specific regulation, there is tension between them. The objectives of the two are not identical. Regulation is conceived to undermine the position of the incumbent and to introduce fragmentation. EU competition law, on the other hand, seeks to preserve the competitive constraints to which firms are subject. As a consequence of this tension, the substantive standards in EU competition law may vary to accommodate the features and demands of network industries. Finally, it appears that EU competition law and sector-specific regulation have a complementary relationship. Sectoral regimes often lack the tools to achieve their objectives. The substantive scope of regulation may be limited, or the range of measures insufficient to address all concerns. EU competition law is a versatile instrument that can remedy some of these gaps. It has proved to be an effective tool to preserve fragmentation in liberalised markets and to manage technological change