Diagonalization of the XXZ Hamiltonian by Vertex Operators

We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.Comment: 65 page

Conversion coefficients and band assignments in Ta-180

The conversion coefficients for several bandhead decays in Ta-180 have been measured using pulsed-beam techniques and the Yb-176(Li-7,3n)Ta-180 reaction. The spin and parity of the 520 keV Intrinsic state is established as 4(+) and several earlier assignments are confirmed. Two-quasiparticle configurations for the 520 and 592 keV states are discussed and following reanalysis of the band properties, a consistent interpretation is reached. The 520 keV 4(+) state is associated with the favored coupling of the nu 1/2(-)[521]x pi 9/2(-)[514] configuration while the 592 keV (5(+)) state is identified with the nu 1/2(-)[510]x pi 9/2(-)[514] configuration

Using a cognitive architecture to examine what develops

Different theories of development propose alternative mechanisms by which development occurs. Cognitive architectures can be used to examine the influence of each proposed mechanism of development while keeping all other mechanisms constant. An ACT-R computational model that matched adult behavior in solving a 21-block pyramid puzzle was created. The model was modified in three ways that corresponded to mechanisms of development proposed by developmental theories. The results showed that all the modifications (two of capacity and one of strategy choice) could approximate the behavior of 7-year-old children on the task. The strategy-choice modification provided the closest match on the two central measures of task behavior (time taken per layer, r = .99, and construction attempts per layer, r = .73). Modifying cognitive architectures is a fruitful way to compare and test potential developmental mechanisms, and can therefore help in specifying “what develops.

Spherical and deformed isomers in Pb-188

Several isomers in Pb-188 have been identified using pulsed beams, the recoil-shadow technique, and the Er-164(Si-28,4n) Pb-188 reaction. Two of the isomers feed the 10(+) state of the yrast sequence and are suggested to be the 11(-) and 12(+) states from oblate and spherical configurations, respectively. The 12(+) isomer is fed weakly by another isomer with a relatively long lifetime, but it has not been characterized. A fourth isomer with a lifetime of about 1.2 mu s leads via a complicated path to the 8(+) and lower spin yrast states. It is a candidate for the K-pi = 8(-), two-quasineutron state which occurs systematically in N = 106 prolate-deformed nuclei, supporting the assumption that the intruding collective well is prolate

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Spherical and deformed structures in Pb189

γ-ray spectroscopy of high-spin states of the neutron-deficient nucleus Pb189 has been conducted with the Gd158(Ar36,5n) and Er164(Si29,4n) reactions. With the first of these, detection of evaporation residues and mass gating were used to unambiguously assign a number of prompt γ-ray transitions to Pb189. With the second reaction and a pulsed beam, an isomer with a mean life of 32 μs was found. Although inconclusive, the available evidence favors identification of the isomer with the 332+ state of the ν(i13/2)-3 configuration. The levels observed below the isomer can be identified with states involving three different structures: the neutron (i13/2)-3 multiplet in the spherical well; a prolate-deformed band involving mixed i13/2 neutron orbitals; and a state with the oblate π(2p-2h)0+ν(i13/ 2)-1 configuration. The evidence for structures associated with different shapes is supported by the observation of E0 components in some of the Jπ→Jπ transitions linking them

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Biochemical Responses of Asparagus to Controlled Atmosphere Storage at 20 Degrees C

In seeking to understand the beneficial effects of controlled atmosphere (CA) storage at 20 degrees C on asparagus (Asparagus officinalis L.), biochemical responses of spear tips stored in air were compared with those of spears stored under CA (2% 02, 10% CO2). CA storage prevented the rapid loss of sucrose, increased acid invertase activity and asparagine accumulation observed in the tips of spears stored in air. CA storage also delayed changes in the levels of glutamine, malic, citric and fumaric acids, compared with those in tips of air-stored spears. Elongation observed in water-fed spears in air was reduced by CA. It is proposed that CA acted by depressing metabolism to such an extent that sucrose levels were maintained in the spear tip and this, in turn, prevented the cascade of metabolic events that contribute to spear deterioration in air