Thermodynamics of the bilinear-biquadratic spin-One heisenberg chain

The magnetic susceptibility and specific heat of the one-dimensional S = 1 bilinear-biquadratic Heisenberg model are calculated using the transfer matrix renormalization group. By comparing the results with the experimental data of LiVGe2O6 measured by Millet et al. [Phys. Rev. Lett. 83, 4176 (1999)], we find that the susceptibility data of this material, after subtracting the impurity contribution, can be quantitatively explained with this model. The biquadratic exchange interaction in this material is found to be ferromagnetic, i.e., with a positive coupling constant.     

Lowering operators for the reduction U(n)↓SO(n)

A complete set of lowering operators is constructed for the reduction U(n)↓SO(n). In an irreducible representation of the unitary group U(n), every vector of maximal weight with respect to the subgroup SO(n) can be obtained using the lowering operators. The formula for the lowering operators is obtained using graphical techniques.     

Graph theory,SO(n) current algebra and the Virasoro master equation

We announce an isomorphism between a set of generically irrational affine-Virasoro constructions onSO(n) and the unlabelled graphs of ordern. On the one hand, the conformal constructions are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. High-level expansion provides a strong argument that each construction is unitary down to some finite critical level.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857     

Effective boundary field theory for a Josephson junction chain with a weak link

We show that a finite Josephson junction (JJ) chain, ending with two bulk superconductors, and with a weak link at its center, may be regarded as a condensed matter realization of a two-boundary sine-Gordon model. Computing the partition function yields a remarkable analytic expression for the DC Josephson current as a function of the phase difference across the chain. We show that, in a suitable range of the chain parameters, there is a crossover of the DC Josephson current from a sinusoidal to a sawtooth behavior, which signals a transition from a regime where the boundary term is an irrelevant operator to a regime where it becomes relevant.     

Renormalized field theory of the critical dynamics ofO(n)-symmetric systems

The critical dynamics of an-component order parameter of anO(n)-symmetric system is analyzed with a Gell'Mann-Low-type renormalization group equation ind=4– dimensions. Dynamical scaling holds forn>3/2+O(). Besides the dynamical exponentz=d/2 the correction exponents to order are found. To the same order the shape function of the dynamical order parameter correlation function is calculated which exhibits fluctuation induced peaks forn3 and extrapolated tod=3.     

Differential operators on quantum spaces for GL q (n) and SO q (n)

We prove that the rings of q-differential operators on quantum planes of the GL _q (n) and SO _q (n) types are isomorphic to the rings of classical differential operators. Also, we construct decompositions of the rings of q-differential operators into tensor products of the rings of q-differential operators with less variables.     

Normal form for the (2;n)-nilpotent vector field, using invariant theory

Here we give an algorithm for finding the normal form of formal power series vector fields on ²ⁿ whose linear terms are the nilpotent matrix made up of 2 × 2 Jordan blocks. The problem is reduced to finding the Stanley decomposition of a bracket algebra, which is then determined using a straightening algorithm. The 4- and 6-dimensional cases are explicitly worked out.     

Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain

We study the magnetic excitation spectrum of the spin-1 chain with Hamiltonian .We focus on the range where the spin chain is in the gapped Haldane phase. The excitation spectrum and static structure factor is studied using direct Lanczos diagonalization of small systems and density-matrix renormalization group techniques combined with the single-mode approximation. The magnon dispersion has a minimum at until a critical value is reached at which the curvature (velocity) vanishes. Beyond this point, which is distinct from the VBS point and the Lifshitz point, the minimum lies at an incommensurate value that goes smoothly to when approaches , the Lai-Sutherland point. The mode remains isolated from the other states: there is no evidence of spinon deconfinement before the point .These findings explain recent observation of the behavior of the magnetization curve for . Received 16 December 1998     

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.     

Effective field theory for disordered magnetic alloys

Disordered alloys of magnetic atoms of two types have been considered within the Ising model based on the calculation and analysis of the distribution function of effective fields acting on magnetic atoms. The Curie temperatures, magnetizations of two magnetic “sublattices,” threshold concentrations of magnetic atoms, and magnetic phase diagrams of alloys have been calculated.     

Effective action for the Yukawa2 quantum field theory

Using a rigorous version of the renormalization group we construct the effective action for theY ₂ model. The construction starts with integrating out the bosonic field which eliminates the large fields problem. Studying the soobtained purely fermionic theory proceeds by a series of convergent perturbation expansions. We show that the continuum limit of the effective action exists and its perturbation expansion is Borel summable.     

Replica symmetric spin glass field theory

A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v)$g(v)$. Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v)$g(v)$ can be derived, whereas it can be exactly computed in the mean field Sherrington–Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d?6$d?6$, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.     

Effective scalar field theory for the electroweak phase transition

We investigate an effective model for the finite-temperature symmetry-restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the (3 + 1)-dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a 3-dimensional O(4) ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean-field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, m_H = 37 GeV, considered in the present investigation, we find a discontinuous symmetry-restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first-order phase transition as compared to the mean-field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first-order transition could result only from non-perturbative effects related to the gauge degrees of freedom.     

SO q (n+1,n−1) as a real form of SO q (2n,ℂ)

Quantum pseudo-orthogonal groups SO _q (n+1,n–1) are defined as real forms of quantum orthogonal groups SO _q (n+1,n–1) by means of a suitable antilinear involution. In particular, the casen=2 gives a quantized Lorentz group.     

Effective field theory in background field gauge

It is shown how to construct effective lagrangians to the two-loop level for non-abelian gauge theories, quantized in background field gauge. This construction is no more difficult than the analogous computation in abelian gauge theories when minimal subtraction is employed. It is argued that for three or more loops, one can no longer separate heavy or mixed light-heavy graphs in an intermediate renormalization, and the more general algorithm presented by us in an earlier work must be employed even in background field gauge.     

Minimization of SO(3) invariant Landau potentials for spin four

The absolute minima for the SO(3) invariant Landau potential for the nine-dimensional (spin-four) irreducible representation is discussed as a function of the coupling constants. The non-maximal D₄ stability group appears. This is studied in relation to Michel's conjecture.     

Effective operators of the spin correlated crystalline electric field

The effective operators of the spin correlated crystal field have been formed by coupling the exchange with the crystal field. The exchange field is a scalar in spin space so the effective operators will still have the same rank as that of the crystal field but will give non-zero matrix elements between the states ^2S+1L_J of the half filled shells, contrary to the zero value obtained for a pure crystal field tensor.     

The goldstone fields of interacting higher spin field theory in AdS(4)

A higher spin field theory on AdS(4) possesses a conformal theory on the boundary R(3) which can be identified with the critical O(N) sigma model of O(N) invariant fields only. The notions of quasiprimary and secondary fields can be carried over to the AdS theory. If de Donder’s gauge is applied, the traceless part of the higher spin field on AdS(4) is quasiprimary and the Goldstone fields are quasiprimary fields to leading order too. Those fields corresponding to the Goldstone fields in the critical O(N) sigma model are odd-rank symmetric tensor currents which vanish in the free-field limit. The text was submitted by the author in English.