512 research outputs found

    Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice

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    We present exact solutions for the zero-temperature partition function of the qq-state Potts antiferromagnet (equivalently, the chromatic polynomial PP) on tube sections of the simple cubic lattice of fixed transverse size Lx×LyL_x \times L_y and arbitrarily great length LzL_z, for sizes Lx×Ly=2×3L_x \times L_y = 2 \times 3 and 2×42 \times 4 and boundary conditions (a) (FBCx,FBCy,FBCz)(FBC_x,FBC_y,FBC_z) and (b) (PBCx,FBCy,FBCz)(PBC_x,FBC_y,FBC_z), where FBCFBC (PBCPBC) denote free (periodic) boundary conditions. In the limit of infinite-length, Lz→∞L_z \to \infty, we calculate the resultant ground state degeneracy per site WW (= exponent of the ground-state entropy). Generalizing qq from Z+{\mathbb Z}_+ to C{\mathbb C}, we determine the analytic structure of WW and the related singular locus B{\cal B} which is the continuous accumulation set of zeros of the chromatic polynomial. For the Lz→∞L_z \to \infty limit of a given family of lattice sections, WW is analytic for real qq down to a value qcq_c. We determine the values of qcq_c for the lattice sections considered and address the question of the value of qcq_c for a dd-dimensional Cartesian lattice. Analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph Km,mK_{m,m}.Comment: 28 pages, latex, six postscript figures, two Mathematica file

    On the Treatment of Neutrino Oscillations Without Resort to Weak Eigenstates

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    We discuss neutrino oscillations in the framework of the quantum field theory without introducing the concept of neutrino weak eigenstates. The external particles are described by wave packets and the different mass eigenstate neutrinos propagate between the production and detection interactions, which are macroscopically localized in space-time. The time-averaged cross section, which is the measurable quantity in the usual experimental setting, is calculated. It is shown that only in the extremely relativistic limit the usual quantum mechanical oscillation probability can be factored out of the cross section.Comment: LaTeX-18pages, JHU-TIPAC-930011,DFTT 22/9

    Infrared Evolution and Phase Structure of a Gauge Theory Containing Different Fermion Representations

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    We study the evolution of an asymptotically free vectorial SU(NN) gauge theory from the ultraviolet to the infrared and the resultant phase structure in the general case in which the theory contains fermions transforming according to several different representations of the gauge group. We discuss the sequential fermion condensation and dynamical mass generation that occur, and comment on the effect of bare fermion mass terms.Comment: 13 pages, late

    Patterns of Dynamical Gauge Symmetry Breaking

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    We construct and analyze theories with a gauge symmetry in the ultraviolet of the form G⊗GbG \otimes G_b, in which the vectorial, asymptotically free GbG_b gauge interaction becomes strongly coupled at a scale where the GG interaction is weakly coupled and produces bilinear fermion condensates that dynamically break the GG symmetry. Comparisons are given between Higgs and dynamical symmetry breaking mechanisms for various models.Comment: 14 pages, late

    Some Exact Results on the Potts Model Partition Function in a Magnetic Field

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    We consider the Potts model in a magnetic field on an arbitrary graph GG. Using a formula of F. Y. Wu for the partition function ZZ of this model as a sum over spanning subgraphs of GG, we prove some properties of ZZ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for ZZ for cyclic strip graphs.Comment: 5 pages, late

    Comparison of Some Exact and Perturbative Results for a Supersymmetric SU(NcN_c) Gauge Theory

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    We consider vectorial, asymptotically free N=1{\cal N}=1 supersymmetric SU(NcN_c) gauge theories with NfN_f copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of NfN_f, compare with exact results. We make use of two-loop and three-loop calculations of the beta function and anomalous dimension of the quadratic chiral super field operator product for this purpose. The specific chiral superfield contents that we consider are NfN_f copies of (i) F+FˉF+\bar F, (ii) AdjAdj, (iii) S2+Sˉ2S_2+\bar S_2, and (iv) A2+Aˉ2A_2 + \bar A_2, where FF, AdjAdj, S2S_2, and A2A_2 denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of Nf,crN_{f,cr} relative to the respective exact results for these representations, i.e., slightly underestimate the interval in NfN_f for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories.Comment: 16 pages, 3 figure

    Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions

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    We consider a vectorial, asymptotically free gauge theory and analyze the effect of higher-loop corrections to the beta function on the evolution of the theory from the ultraviolet to the infrared. We study the case in which the theory contains NfN_f copies of a fermion transforming according to the fundamental representation and several higher-dimensional representations of the gauge group. We also calculate higher-loop values of the anomalous dimension of the mass, γm\gamma_m of ψˉψ\bar\psi\psi at the infrared zero of the beta function. We find that for a given theory, the values of γm\gamma_m calculated to three- and four-loop order, and evaluated at the infrared zero computed to the same order, tend to be somewhat smaller than the value calculated to two-loop order. The results are compared with recent lattice simulations.Comment: 22 pages, latex, matches Phys. Rev. D publicatio

    Magnetothermodynamics: Measurements Of The Thermodynamic Properties In A Relaxed Magnetohydrodynamic Plasma

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    We have explored the thermodynamics of compressed magnetized plasmas in laboratory experiments and we call these studies ‘magnetothermodynamics’. The experiments are carried out in the Swarthmore Spheromak eXperiment device. In this device, a magnetized plasma source is located at one end and at the other end, a closed conducting can is installed. We generate parcels of magnetized plasma and observe their compression against the end wall of the conducting cylinder. The plasma parameters such as plasma density, temperature and magnetic field are measured during compression using HeNe laser interferometry, ion Doppler spectroscopy and a linear dot{B} probe array, respectively. To identify the instances of ion heating during compression, a PV diagram is constructed using measured density, temperature and a proxy for the volume of the magnetized plasma. Different equations of state are analysed to evaluate the adiabatic nature of the compressed plasma. A three-dimensional resistive magnetohydrodynamic code (NIMROD) is employed to simulate the twisted Taylor states and shows stagnation against the end wall of the closed conducting can. The simulation results are consistent to what we observe in our experiments

    Simultaneous Extraction of the Fermi constant and PMNS matrix elements in the presence of a fourth generation

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    Several recent studies performed on constraints of a fourth generation of quarks and leptons suffer from the ad-hoc assumption that 3 x 3 unitarity holds for the first three generations in the neutrino sector. Only under this assumption one is able to determine the Fermi constant G_F from the muon lifetime measurement with the claimed precision of G_F = 1.16637 (1) x 10^-5 GeV^-2. We study how well G_F can be extracted within the framework of four generations from leptonic and radiative mu and tau decays, as well as from K_l3 decays and leptonic decays of charged pions, and we discuss the role of lepton universality tests in this context. We emphasize that constraints on a fourth generation from quark and lepton flavour observables and from electroweak precision observables can only be obtained in a consistent way if these three sectors are considered simultaneously. In the combined fit to leptonic and radiative mu and tau decays, K_l3 decays and leptonic decays of charged pions we find a p-value of 2.6% for the fourth generation matrix element |U_{e 4}|=0 of the neutrino mixing matrix.Comment: 19 pages, 3 figures with 16 subfigures, references and text added refering to earlier related work, figures and text in discussion section added, results and conclusions unchange
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