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

Alometrías intertaxónicas y ontogenéticas entre el área del septo y el volumen del fragmocono en cefalopodos con concha espiral actuales y extintos

La interpretación funcional del replegamiento periférico de los septos de los ammonoideos constituye todo un reto dada la inexistencia de representantes actuales del grupo y, por consiguiente, la imposibilidad de experimentación directa. Por tal motivo las líneas de evidencia se han de basar en gran medida en comparaciones con otros cefalópodos camerados actuales. En este trabajo se comparan las alometrías ontogenéticas que siguen el área septal respecto al volumen del fragmocono en cefalópodos con concha espiral (interna o externa) con las obtenidas para ammonoideos adultos del Jurásico tardío. Las similitudes entre los coeficientes alométricos indican que el aumento de superficie que supone replegar los septos no aparenta ser muy diferente en las primeras etapas del crecimiento de los ammonoideos del de otros cefalópodos con concha espiral. Por el contrario, las discrepancias con los coeficientes alométricos para los ammonoideos adultos parecen apuntar a que la complejidad septal no se alcanza por una mera extrapolación de la ontogenia.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The influence of skull shape modularity on internal skull structures: a 3D-Pilot study using bears

In order to capture the phenotypic variation of the internal skull structures, such as the sinuses or the brain, it is necessary to perform CT scans in a large number of specimens, which is difficult and expensive. Therefore, while the external morphology of the mammalian cranium has been the subject of many morphometric studies, the internal structures of the cranium have been comparatively less studied. Here, we explore how the variation of external shape reflects the morphology of internal structures. We use the family Ursidae (Carnivora, Mammalia) as a case study because bears have a wide variability of cranial morphologies in part associated with different trophic ecologies. To do this, we digitized a set of landmarks in 3D with a Microscribe G2X from the external surface of the cranium in a wide sample of bears. Additionally, the crania of seven bear species were CT-scanned and prepared digitally to visualize the 3D models of the external cranium morphology and of internal structures. Subsequently, we divided the landmarks into two modules, splanchnocranium and neurocranium, and we perform a two-block partial least squares analysis (2B PLS) to explore the intraspecific (static) morphological changes associated with the covariation between them. These morphological changes were visualized using the morphing technique with the 3D models, looking at both the external shape and the internal structures. In addition, we inferred the volume of the sinuses and of the brain in each hypothetical model. Our results show that the first two PLS axes are associated externally with changes in the basicranial angle, face length and cranium height and width. Concerning the internal structures, there are parallel changes in dorso-ventral and medio-lateral expansion of sinuses and brain, accompanied by their corresponding changes in volume. In contrast, the third PLS axis is related to opposite changes in the volume of sinuses and brain. These preliminary results suggest that the opposite relationship between sinuses and brain volumes in the bear cranium is not as evident as expected, at least at intraspecific level.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Body-axis organization in tetrapods: a model-system to disentangle the developmental origins of convergent evolution in deep time

Convergent evolution is a central concept in evolutionary theory but the underlying mechanism has been largely debated since On the Origin of Species. Previous hypotheses predict that developmental constraints make some morphologies more likely to arise than others and natural selection discards those of the lowest fitness. However, the quantification of the role and strength of natural selection and developmental constraint in shaping convergent phenotypes on macroevolutionary timescales is challenging because the information regarding performance and development is not directly available. Accordingly, current knowledge of how embryonic development and natural selection drive phenotypic evolution in vertebrates has been extended from studies performed at short temporal scales. We propose here the organization of the tetrapod body-axis as a model system to investigate the developmental origins of convergent evolution over hundreds of millions of years. The quantification of the primary developmental mechanisms driving body-axis organization (i.e. somitogenesis, homeotic effects and differential growth) can be inferred from vertebral counts, and recent techniques of three-dimensional computational biomechanics have the necessary potential to reveal organismal performance even in fossil forms. The combination of both approaches offers a novel and robust methodological framework to test competing hypotheses on the functional and developmental drivers of phenotypic evolution and evolutionary convergence

Spontaneous plaquette dimerization in the J1−J2J_1-J_2 Heisenberg model

We investigate the non magnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected `plaquette RVB', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for $J_2/J_1 \simeq 0.5$.Comment: 4 pages, 5 postscript figure

Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems

The Resonating Valence Bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough ``quantum frustration''. This scenario, proposed long time ago but never confirmed by microscopic calculations, is very strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the $J_1{-}J_2$ Heisenberg model for $0.4 \lesssim J_2/J_1\lesssim 0.5$. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.Comment: 4 Pages, 5 figures, accepted for publication in PR

New quantum phase transitions in the two-dimensional J1-J2 model

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the J1-J2 model, in two dimensions. Two quantum phase transitions in the model are already known: the second order transition from the Neel state to the spin liquid state at (J_2/J_1)_{c2}=0.38, and the first order transition from the spin liquid state to the collinear state at (J_2/J_1)_{c4}=0.60. We have found evidence for two new second order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette type modulation at (J_2/J_1)_{c3}=0.50(2), and the transition from the simple Neel state to the Neel state with spin columnar dimerization at (J_2/J_1)_{c1}=0.34(4). We also present an independent calculation of (J_2/J_1)_{c2}=0.38 using a new approach.Comment: 3 pages, 5 figures; added referenc

Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet

We study the spin-$1\over2$ Heisenberg antiferromagnet with an antiferromagnetic $J_3$ (third nearest neighbor) interaction on a square lattice. We numerically diagonalize this ``$J_1$-$J_3$'' model on clusters up to 32-sites and search for novel ground state properties as the frustration parameter $J_3/J_1$ changes. For ``larger'' $J_3/J_1$ we find enhancement of incommensurate spin order, in agreement with spin-wave, large-$N$ expansions, and other predictions. But for intermediate $J_3/J_1$, the low lying excitation energy spectrum suggests that this incommensurate order is short-range. In the same region, the first excited state has the symmetries of the columnar dimer (spin-Peierls) state. The columnar dimer order parameter suggests the presence of long-range columnar dimer order. Hence, this spin-Peierls state is the best candidate for the ground state of the $J_1$-$J_3$ model in an intermediate $J_3/J_1$ region.Comment: RevTeX file with five postscript figures uuencode

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

Evolution of Ultracold, Neutral Plasmas

We present the first large-scale simulations of an ultracold, neutral plasma, produced by photoionization of laser-cooled xenon atoms, from creation to initial expansion, using classical molecular dynamics methods with open boundary conditions. We reproduce many of the experimental findings such as the trapping efficiency of electrons with increased ion number, a minimum electron temperature achieved on approach to the photoionization threshold, and recombination into Rydberg states of anomalously-low principal quantum number. In addition, many of these effects establish themselves very early in the plasma evolution ($\sim$ ns) before present experimental observations begin.Comment: 4 pages, 3 figures, submitted to PR