Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.Comment: 12 pages, 12 figure

Effect of nitrogen, phosphorous, potassium, plant growth regulator and artificial lodging on grain yield and grain quality of a landrace of barley

Landraces of different crops are still preferred due to their stable yields under low inputs and adverse climatic conditions to which most modern varieties are not adapted. In the UK, a landrace of barley called Bere is currently grown in extreme climatic conditions of Orkney to which most of the modern varieties are not adapted. Although this landrace is probably the oldest barley under cultivation in the UK, very little research has been conducted. In this paper the effects of nitrogen, phosphorous, potassium, plant growth regulator and artificial lodging on grain yield and quality of Bere were investigated in the Orkney\u27s short growing season. Higher nitrogen application resulted in a higher lodging incidence but grain yield was not reduced by the severity of lodging. The artificial lodging applied at Zadoks growth stage 77 resulted in the greatest yield losses which indicated that control measures may be required to avoid lodging at this critical growth stage. Phosphorous and potassium had no significant effect on lodging resistance. Whilst plant growth regulator improved lodging resistance it was less effective in controlling lodging at the highest nitrogen level (90 kg ha-1). The trials indicated that higher level of N caused marginal increase in grain yield when nitrogen level was raised from 45 kg to 90 kg ha-1. This tended to suggest the use of medium N-level (45 kg N ha-1) for producing Bere. Plant growth regulator increased lodging resistance but had an inconsistent effect on grain yield. This study recommended the use of plant growth regulator as a means of easing harvesting rather than for enhancing yield and quality. The study concluded that phosphorous and potassium could be used to improve disease resistance and grain yield but not for lodging control

The Higgs sector of the complex MSSM at two-loop order: QCD contributions

Results are presented for the leading two-loop contributions of O(alpha_t alpha_s) to the masses and mixing effects in the Higgs sector of the MSSM with complex parameters. They are obtained in the Feynman-diagrammatic approach using on-shell renormalization. The full dependence on all complex phases is taken into account. The renormalization of the appropriate contributions of the Higgs-boson sector and the scalar top and bottom sector is discussed. Our numerical analysis for the lightest MSSM Higgs-boson mass is based on the new two-loop corrections, supplemented by the full one-loop result. The corrections induced by the phase variation in the scalar top sector are enhanced by the two-loop contributions. We find that the corresponding shift in M_h1 can amount to 5 GeV.Comment: 15 pages, 7 figures; minor changes; published versio

Time-resolved spectroscopy of the primary photosynthetic processes of membrane-bound reaction centers from an antenna-deficient mutant of Rhodobacter capsulatus

The primary photosynthetic reactions in whole membranes of the antenna-deficient mutant strain U43 (pTXA6–10) of Rhodobacter capsulatus are studied by transient absorption and emission spectroscopy with subpicosecond time resolution. Extensive similarities between the transient absorption data on whole membranes and on isolated reaction centers support the idea that the primary processes in isolated reaction centers are not modified by the isolation procedure

Direct Measurement of the Top Quark Charge at Hadron Colliders

We consider photon radiation in tbar-t events at the upgraded Fermilab Tevatron and the CERN Large Hadron Collider (LHC) as a tool to measure the electric charge of the top quark. We analyze the contributions of tbar-t-gamma production and radiative top quark decays to p-p, pbar-p -> gamma l^+/- nu bbar-b jj, assuming that both b-quarks are tagged. With 20~fb^{-1} at the Tevatron, the possibility that the ``top quark'' discovered in Run I is actually an exotic charge -4/3 quark can be ruled out at the 95% confidence level. At the LHC, it will be possible to determine the charge of the top quark with an accuracy of about 10%.Comment: Revtex, 24 pages, 2 tables, 9 figure

Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE

Testing SUSY

If SUSY provides a solution to the hierarchy problem then supersymmetric states should not be too heavy. This requirement is quantified by a fine tuning measure that provides a quantitative test of SUSY as a solution to the hierarchy problem. The measure is useful in correlating the impact of the various experimental measurements relevant to the search for supersymmetry and also in identifying the most sensitive measurements for testing SUSY. In this paper we apply the measure to the CMSSM, computing it to two-loop order and taking account of current experimental limits and the constraint on dark matter abundance. Using this we determine the present limits on the CMSSM parameter space and identify the measurements at the LHC that are most significant in covering the remaining parameter space. Without imposing the LEP Higgs mass bound we show that the smallest fine tuning (1:13) consistent with a relic density within the WMAP bound corresponds to a Higgs mass of 114$\pm$2 GeV. Fine tuning rises rapidly for heavier Higgs.Comment: 12 pages, 7 figures; references added, figures updated for extended parameter space sca

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.Comment: 13 pages, 17 figure, 0 table

Zeros of Jones Polynomials for Families of Knots and Links

We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial. For each of these families we determine the zeros of the Jones polynomial, including the accumulation set in the limit of infinitely many crossings. A discussion is also given of the calculation of Jones polynomials for non-alternating links.Comment: 30 pages, latex, 9 postscript figures; minor rewording on a reference, no changes in result