Fragmentation in the Governance of EU External Relations: Legal Institutional Dilemmas and the New Constitution for Europe

The European Union, an Ongoing Process of Integration contains 27 original contributions authored by prominent EU lawyers from academia and practice and concentrates on the three main areas of European integration that mark the career path of Alfred E. Kellermann: institutional and constitutional aspects (part I), general principles and substantive aspects (part II), and new Member States and Eastern Europe (part III). The contributions included in this Liber Amicorum vary from thematic in-depth studies to studies of a comparative nature. Their themes cover, inter alia, the structure of the Union according to the Constitution for Europe, the changes and challenges with which the Union¿s institutions are faced, including the creation of the positions of the President of the European Council and the Union Minister for Foreign Affairs, the future paths of flexibility (enhanced cooperation, partial agreements and pioneer groups), the role of national competition authorities and national courts under Regulation 1/2003, the constitutional preparation for EU accession in the new Member States, and the influence of European integration on the development of law in Russia. All contributions have been written in honour of Alfred E. Kellermann. Born in The Hague, raised in Switzerland during the Second World War and having studied and trained at Leiden University and at the European Commission¿s Legal Service in Brussels in the founding years of the European integration process, Doctor Honoris Causa Alfred E. Kellermann is a European by nature and vocation. For almost forty years, Alfred E. Kellermann has worked for the T.M.C. Asser Institute in The Hague. For many, he has become the face of the Institute in the Netherlands and abroad. This is the result of his work as a lecturer and consultant in EU law in countless short and long-term projects all over Europe, including Russia. Perhaps his finest accomplishment in raising awareness and expertise in the law of the European Union concerns the organisation of the famous `Asser Colloquia¿ on EU law and the publication of their proceedings

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.Comment: 12 pages, 15 figure

Pairing and chiral spin density wave instabilities on the honeycomb lattice: a comparative quantum Monte Carlo study

Using finite-temperature determinantal quantum Monte Carlo calculations, we re-examine the pairing susceptibilities in the Hubbard model on the honeycomb lattice, focusing on doping levels onto and away from the van Hove singularity (VHS) filling. For this purpose, electronic densities of $0.75$ (at the hole-doping VHS) and $0.4$ (well below the VHS) are considered in detail, where due to a severe sign problem at strong coupling strengths, we focus on the weak interaction region of the Hubbard model Hamiltonian. From analyzing the temperature dependence of pairing susceptibilities in various symmetry channels, we find the singlet $d$+$id$-wave to be the dominant pairing channel both at and away from the VHS filling. We furthermore investigate the electronic susceptibility to a specific chiral spin density wave (SDW) order, which we find to be similarly relevant at the VHS, while it extenuates upon doping away from the VHS filling.Comment: 8 pages, 14 figures. Accepted by PRB. Two figures added, more lattice sizes studie

Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice

The antiferromagnetic Ising model on the pyrochlore lattice exhibits a quantum phase transition in an applied transverse field from the low-field quantum spin-ice phase to the high-field polarized regime. Recent field-theoretical analysis and series expansion results indicate this to be a discontinuous, first-order transition. Here, we explore this transition using quantum Monte Carlo simulations in order to assess this scenario and study the thermodynamic properties in the vicinity of the quantum phase transition. For this purpose, we also consider several variants of extended cluster-update schemes for the transverse field Ising antiferromagnet on frustrated lattices and compare their performance to the conventional bond-based algorithm for the transverse field Ising model on the pyrochlore lattice.Comment: 13 pages, 15 figures, v2: as publishe

Magnetic Field Induced Ordering in Quasi-One-Dimensional Quantum Magnets

Three-dimensional magnetic ordering transitions are studied theoretically in strongly anisotropic quantum magnets. An external magnetic field can drive quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus inducing long-range three-dimensional magnetic ordering due to weak residual magnetic coupling between the subsystems. Compounds with higher spin degrees of freedom, such as N-leg spin-1/2 ladders, are shown to have cascades of ordering transitions. At high magnetic fields, zero-point fluctuations within the quasi-1D subsystems are suppressed, causing quantum corrections to the ordering temperature to be reduced.Comment: RevTex, 12 pages with 4 figure

Thermal Ising transitions in the vicinity of two-dimensional quantum critical points

The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the ${\it chiral}$ Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case we extract values of the critical exponents $\nu$ and $\eta$, related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground state quantum Monte Carlo calculations as well as analytical approaches.Comment: 11 pages, 13 figure

Lecture notes on ridge regression

The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a penalty (i.e. a function of regression coefficients). The ridge penalty is the sum of squared regression coefficients, giving rise to ridge regression. Here many aspect of ridge regression are reviewed e.g. moments, mean squared error, its equivalence to constrained estimation, and its relation to Bayesian regression. Finally, its behaviour and use are illustrated in simulation and on omics data. Subsequently, ridge regression is generalized to allow for a more general penalty. The ridge penalization framework is then translated to logistic regression and its properties are shown to carry over. To contrast ridge penalized estimation, the final chapter introduces its lasso counterpart

Critical Entropy of Quantum Heisenberg Magnets on Simple-Cubic Lattices

We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using optimized extended ensemble quantum Monte Carlo simulations, we extract the entropy at the critical temperature for magnetic order from a finite-size scaling analysis. For the antiferromagnetic case, the critical entropy density equals 0.341(5)$k_B$, whereas for the ferromagnet, a larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results to estimates put forward recently in studies assessing means of realizing the antiferromagnetic N\'eel state in ultra-cold fermion gases in optical lattices.Comment: 3 pages, 2 figures; published versio