Low temperature broken symmetry phases of spiral antiferromagnets

We study Heisenberg antiferromagnets with nearest- (J1) and third- (J3) neighbor exchange on the square lattice. In the limit of large spin S, there is a zero temperature (T) Lifshitz point at J3 = (1/4) J1, with long-range spiral spin order at T=0 for J3 > (1/4) J1. We present classical Monte Carlo simulations and a theory for T>0 crossovers near the Lifshitz point: spin rotation symmetry is restored at any T>0, but there is a broken lattice reflection symmetry for 0 <= T < Tc ~ (J3-(1/4) J1) S^2. The transition at T=Tc is consistent with Ising universality. We also discuss the quantum phase diagram for finite S.Comment: 4 pages, 5 figure

Spin-lattice coupling in frustrated antiferromagnets

We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks the inversion symmetry and gives rise to a chiral pyrochlore lattice, in which frustrated bonds form helices with a definite handedness. The chirality is transferred to the spin system through spin-orbit coupling, resulting in a long-period spiral state, as observed in spinel CdCr2O4. We discuss explicit models of spin-lattice coupling using local phonon modes, and their applications in other frustrated magnets.Comment: 23 pages, 6 figures. Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mil

Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets

We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of the triangular and $J_1{-}J_2$ Heisenberg antiferromagnets, using finite-size spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In the triangular Heisenberg antiferromagnet, by performing a systematic size-scaling analysis, we have obtained strong evidences for a gapless spectrum and a finite value of the thermodynamic order parameter, thus confirming the existence of long-range N\'eel order.The good agreement between the finite-size spin-wave results and the exact and quantum Monte Carlo data also supports the reliability of the spin-wave expansion to describe both the ground state and the low-energy spin excitations of the triangular Heisenberg antiferromagnet. In the $J_1{-}J_2$ Heisenberg model, our results indicate the opening of a finite gap in the thermodynamic excitation spectrum at $J_2/J_1 \simeq 0.4$, marking the melting of the antiferromagnetic N\'eel order and the onset of a non-magnetic ground state. In order to characterize the nature of the latter quantum-disordered phase we have computed the susceptibilities for the most important crystal symmetry breaking operators. In the ordered phase the effectiveness of the spin-wave theory in reproducing the low-energy excitation spectrum suggests that the uniform spin susceptibility of the model is very close to the linear spin-wave prediction.Comment: Review article, 44 pages, 18 figures. See also PRL 87, 097201 (2001

Model-free moments: predictability of STOXX Europe 600 Oil & Gas future returns

The relationship between prices and volatility of energy assets (primarily oil and gas) is of paramount importance for investors and policy makers. We construct a volatility index for the European oil and gas market based on a model-free approach to obtain a European counterpart of US volatility indices for the energy market, such as the CBOE Crude Oil Volatility Index (OVX). Given that investors are averse to volatility of losses, but appreciate volatility of gains, we also derive risk measures that focus on positive and negative returns and their imbalance. We assess whether the constructed indices have predictive power on future returns. We show that in the medium term all the risk indices behave as market greed indicators, whereas in the short term they behave as fear indicators since rises in risk indices are linked with negative returns. The implications for investors and policy-makers are outlined

Suppression of Dimer Correlations in the Two-Dimensional J1J_1-J2J_2 Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter

Climate risk definition and measures: asset pricing models and stock returns

The aim of this study is to examine the literature on climate risk definition and measures and the impact of climate risk on stock returns. We review how asset pricing models (and their testable implications) consider climate risk as a residual systemic risk driver in excess of either standard market risk factors or latent factors identified with business and financial cycles. Firms less exposed to transition risk, in equilibrium, should face a lower cost of equity financing, given an expected return lower than the one associated with pollutant firms. The existence of a recent outperformance of realized returns on green stocks can be reconciled with unexpected shifts in investors tastes for green assets. Finally, we identify some issues regarding the empirical approach and suggest several potential areas for future research

Inhomogeneity Induces Resonance Coherence Peaks in Superconducting BSCCO

In this paper we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped BSCCO in zero field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2 xi_0 * 2 xi_0 patch with an enhanced or supressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.Comment: 4 pages, 3 figure

Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group

In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets, symmetries, and collective dynamics. This last item allows to study integrability as inherited from a system on the whole cotangent bundle, leading in a natural way to the AKS theory for integrable systems