A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY Quantum Chain in a Magnetic Field

We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the SU(1/1) superalgebra. One is led to an extension of the braid group and the Hecke algebra which reduce to the known ones when the two parameter coincide. The physical significance of the two parameters is discussed.Comment:

The Density Matrix Renormalization Group Method applied to Interaction Round a Face Hamiltonians

Given a Hamiltonian with a continuous symmetry one can generally factorize that symmetry and consider the dynamics on invariant Hilbert Spaces. In Statistical Mechanics this procedure is known as the vertex-IRF map, and in certain cases, like rotational invariant Hamiltonians, can be implemented via group theoretical techniques. Using this map we translate the DMRG method, which applies to 1d vertex Hamiltonians, into a formulation adequate to study IRF Hamiltonians. The advantage of the IRF formulation of the DMRG method ( we name it IRF-DMRG), is that the dimensions of the Hilbert Spaces involved in numerical computations are smaller than in the vertex-DMRG, since the degeneracy due to the symmetry has been eliminated. The IRF-DMRG admits a natural and geometric formulation in terms of the paths or string algebras used in Exactly Integrable Systems and Conformal Field Theory. We illustrate the IRF-DMRG method with the study of the SOS model which corresponds to the spin 1/2 Heisenberg chain and the RSOS models with Coxeter diagram of type A, which correspond to the quantum group invariant XXZ chain.Comment: 22 pages, Latex, 18 figures in Postscript file

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure

Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q

The Q-state Potts model can be extended to noninteger and even complex Q in the FK representation. In the FK representation the partition function,Z(Q,a), is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this polynomial,Phi(b,c), are the number of graphs on the lattice consisting of b bonds and c connected clusters. We introduce the random-cluster transfer matrix to compute Phi exactly on finite square lattices. Given the FK representation of the partition function we begin by studying the critical Potts model Z_{CP}=Z(Q,a_c), where a_c=1+sqrt{Q}. We find a set of zeros in the complex w=sqrt{Q} plane that map to the Beraha numbers for real positive Q. We also identify tilde{Q}_c(L), the value of Q for a lattice of width L above which the locus of zeros in the complex p=v/sqrt{Q} plane lies on the unit circle. We find that 1/tilde{Q}_c->0 as 1/L->0. We then study zeros of the AF Potts model in the complex Q plane and determine Q_c(a), the largest value of Q for a fixed value of a below which there is AF order. We find excellent agreement with Q_c=(1-a)(a+3). We also investigate the locus of zeros of the FM Potts model in the complex Q plane and confirm that Q_c=(a-1)^2. We show that the edge singularity in the complex Q plane approaches Q_c as Q_c(L)~Q_c+AL^-y_q, and determine the scaling exponent y_q. Finally, by finite size scaling of the Fisher zeros near the AF critical point we determine the thermal exponent y_t as a function of Q in the range 2<Q<3. We find that y_t is a smooth function of Q and is well fit by y_t=(1+Au+Bu^2)/(C+Du) where u=u(Q). For Q=3 we find y_t~0.6; however if we include lattices up to L=12 we find y_t~0.50.Comment: to appear in Physical Review

Edge states and conformal boundary conditions in super spin chains and super sigma models

The sigma models on projective superspaces CP^{N+M-1|N} with topological angle theta=pi mod 2pi flow to non-unitary, logarithmic conformal field theories in the low-energy limit. In this paper, we determine the exact spectrum of these theories for all open boundary conditions preserving the full global symmetry of the model, generalizing recent work on the particular case M=0 [C. Candu et al, JHEP02(2010)015]. In the sigma model setting, these boundary conditions are associated with complex line bundles, and are labelled by an integer, related with the exact value of theta. Our approach relies on a spin chain regularization, where the boundary conditions now correspond to the introduction of additional edge states. The exact values of the exponents then follow from a lengthy algebraic analysis, a reformulation of the spin chain in terms of crossing and non-crossing loops (represented as a certain subalgebra of the Brauer algebra), and earlier results on the so-called one- and two-boundary Temperley Lieb algebras (also known as blob algebras). A remarkable result is that the exponents, in general, turn out to be irrational. The case M=1 has direct applications to the spin quantum Hall effect, which will be discussed in a sequel.Comment: 50 pages, 18 figure

Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field

The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the $Q>2$ Potts models in the complex temperature plane with nonzero external magnetic field $H_q$. Unlike the Ising model for $H_q\ne0$ which has only a non-physical critical point (the Fisher edge singularity), the $Q>2$ Potts models have physical critical points for $H_q<0$ as well as the Fisher edge singularities for $H_q>0$. For $H_q<0$ the cross-over of the Fisher zeros of the $Q$-state Potts model into those of the ($Q-1$)-state Potts model is discussed, and the critical line of the three-state Potts ferromagnet is determined. For $H_q>0$ we investigate the edge singularity for finite lattices and compare our results with high-field, low-temperature series expansion of Enting. For $3\le Q\le6$ we find that the specific heat, magnetization, susceptibility, and the density of zeros diverge at the Fisher edge singularity with exponents $\alpha_e$, $\beta_e$, and $\gamma_e$ which satisfy the scaling law $\alpha_e+2\beta_e+\gamma_e=2$.Comment: 24 pages, 7 figures, RevTeX, submitted to Physical Review

Exact S-matrices for supersymmetric sigma models and the Potts model

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.Comment: 32 pages, 8 figure

Central sensitization: a biopsychosocial explanation for chronic widespread pain in patients with fibromyalgia and chronic fatigue syndrome

In addition to the debilitating fatigue, the majority of patients with chronic fatigue syndrome (CFS) experience chronic widespread pain. These pain complaints show the greatest overlap between CFS and fibromyalgia (FM). Although the literature provides evidence for central sensitization as cause for the musculoskeletal pain in FM, in CFS this evidence is currently lacking, despite the observed similarities in both diseases. The knowledge concerning the physiological mechanism of central sensitization, the pathophysiology and the pain processing in FM, and the knowledge on the pathophysiology of CFS lead to the hypothesis that central sensitization is also responsible for the sustaining pain complaints in CFS. This hypothesis is based on the hyperalgesia and allodynia reported in CFS, on the elevated concentrations of nitric oxide presented in the blood of CFS patients, on the typical personality styles seen in CFS and on the brain abnormalities shown on brain images. To examine the present hypothesis more research is required. Further investigations could use similar protocols to those already used in studies on pain in FM like, for example, studies on temporal summation, spatial summation, the role of psychosocial aspects in chronic pain, etc

Going up the Andes: patterns and drivers of non-native plant invasions across latitudinal and elevational gradients

The Andes mountain range in South America has a high level of endemism and is a major source of ecosystem services. The Andes is increasingly threatened by anthropogenic disturbances that have allowed the establishment of non-native plants, mainly in the lower elevation areas. However, synergies between climate change and anthropogenic pressure are promoting the spread of non-native plants to higher elevation areas. In this article, we evaluate and identify the main non-native plants invading Andean ecosystems, and assess their taxonomic families, growth forms and distribution patterns. Based on a systematic literature review, we identified the importance of climatic and anthropogenic factors as drivers of non-native species establishment in Andean ecosystems and the main impacts of non-native plants in the Andes. We then identified research gaps across each biogeographic region in the Andes. Finally, we highlight key elements to better tackle the problem of non-native plant invasions in Andean ecosystems, including the need for a systematic monitoring of invasion patterns and spread (e.g. MIREN protocol) and a common policy agenda across international borders for the prevention and management of non-native plants in this highly vulnerable region.Fil: Fuentes Lillo, Eduardo. Universidad de Concepción; Chile. Universiteit Antwerp; BélgicaFil: Lembrechts, Jonas J.. Universiteit Antwerp; BélgicaFil: Barros, Ana Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; ArgentinaFil: Aschero, Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; ArgentinaFil: Bustamante, Ramiro O.. Universidad de Chile; ChileFil: Cavieres, Lohengrin A.. Universidad de Concepción; ChileFil: Clavel, Jan. Universiteit Antwerp; BélgicaFil: Herrera, Ileana. Universidad Espíritu Santo; EcuadorFil: Jiménez, Alejandra. Universidad de Concepción; ChileFil: Tecco, Paula Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Hulme, Philip E.. Lincoln University.; Nueva ZelandaFil: Nuñez, Martin Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; ArgentinaFil: Rozzi, Ricardo. University of North Texas; Estados UnidosFil: García, Rafael A.. Universidad de Concepción; ChileFil: Simberloff, Daniel. University of Tennessee; Estados UnidosFil: Nijs, Ivan. Universiteit Antwerp; BélgicaFil: Pauchard, Aníbal. Universidad de Concepción; Chil

Quantum criticalities in a two-leg antiferromagnetic S=1/2 ladder induced by a staggered magnetic field

We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility and the string order parameter.Comment: 29 pages of revtex, 10 figure