Lifshitz-point critical behaviour to O(ϵ2){\boldsymbol{O(\epsilon^2)}}

We comment on a recent letter by L. C. de Albuquerque and M. M. Leite (J. Phys. A: Math. Gen. 34 (2001) L327-L332), in which results to second order in $\epsilon=4-d+\frac{m}{2}$ were presented for the critical exponents $\nu_{{\mathrm{L}}2}$, $\eta_{{\mathrm{L}}2}$ and $\gamma_{{\mathrm{L}}2}$ of d-dimensional systems at m-axial Lifshitz points. We point out that their results are at variance with ours. The discrepancy is due to their incorrect computation of momentum-space integrals. Their speculation that the field-theoretic renormalization group approach, if performed in position space, might give results different from when it is performed in momentum space is refuted.Comment: Latex file, uses the included iop stylefiles; Uses the texdraw package to generate included figure

Effects of static magnetic field in Saccharomyces cerevisiae cultures under aerobic and anaerobic conditions

Magnetic fields have been studied by many researchers as an agent that provides changes in the metabolism of microorganisms. The effects in biological systems are produced by a relative movement between mobile ions or intracellular free electrons and the magnetic field, which can generate electric fields within a cell. Despite of the interaction mechanism to be yet unclear, is known also that the direct action of magnetism cause changes in the conformational shape of cell proteins, altering its functions. The purpose of this research was to investigate whether static magnetic field (SMF) could be applied to increasing ethanol yield by S. cerevisiae and verifying the biological effects on growth stimulation or inhibition. The influence of aerobic and anaerobic conditions and the ability of the cells to induce their defensive enzymes were also explored. Batch fermentations of S. cerevisiae were conducted for 26 h, in YPD medium, in hyperbaric bioreactor (Parr 4563, Parr Instruments, USA) with 5 NdFeB magnets, with an average flux of 120 mT (measured by a PHYWI Teslameter, USA). The magnets were enclosed into a transparent flat polyethylene case with 4.0 x 3.5 cm and 1.3 cm width. All magnets were disposed with the same polarity, so when closed the case every one showed similar north or south poles at each face of the case. As they repelled each one, the magnets maintained the maximal distance between them, in an “X” disposition, with a magnet in the center. Controls were performed in the same manner without magnets. To investigate the effects of gas, aerobic and anaerobic conditions trials were performed under air (1 bar and 5 bar) and nitrogen (1 bar). An increase of the cell dry weight and specific growth rate, under aerobic conditions (5 bar of total air pressure), of approximately 2-fold was obtained compared with the experiments exposed to nitrogen, for both magnetized and non-magnetized cultures. The cellular growth was not stimulated by the application of SMF. In fact, an improvement of 2-fold in specific growth rate was obtained in the control group, for aerobic and anaerobic conditions. An increase of approximately 3-fold in biomass yield was obtained in aerobic cultures compared with anaerobic. The biomass yield of exposed group to SMF was similar to non-exposed one under 5 bar of air pressure and in nitrogen cultures. On the other hand, a stimulation of ethanol production was obtained in magnetized cultures relatively to those of the controls, for both aerobic and anaerobic conditions. Generally, antioxidant enzymes were induced by total air. An increase of the SOD specific activity in magnetized cultures was obtained compared with the control experiments. Also, the SMF exposed cultures reached the highest values of the catalase specific activity. However, SMF exposure led to a decrease in the glutathione reductase activity. The marker malondialdehyde (MDA) is certainly the most widely used to assess the lipid peroxidation processes. The use of anaerobic conditions resulted in a reduction of MDA levels, for both exposed and nonexposed groups. Generally, the MDA concentration was similar for both magnetized and nonmagnetized cultures. This work shows that magnetic fields can be applied as a controlling factor of S. cerevisiae fermentations for ethanol or enzymes production

Anisotropic Lifshitz Point at O(ϵL2)O(\epsilon_L^2)

We present the critical exponents $\nu_{L2}$, $\eta_{L2}$ and $\gamma_{L}$ for an $m$-axial Lifshitz point at second order in an $\epsilon_{L}$ expansion. We introduced a constraint involving the loop momenta along the $m$-dimensional subspace in order to perform two- and three-loop integrals. The results are valid in the range $0 \leq m < d$. The case $m=0$ corresponds to the usual Ising-like critical behavior.Comment: 10 pages, Revte

Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order (8−d)2\boldsymbol{(8-d)^2}

A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents $\nu$ and $\eta$, the crossover exponent $\phi$, as well as the (related) wave-vector exponent $\beta_q$, and the correction-to-scaling exponent $\omega$ to second order in $\epsilon_8=8-d$. These are compared with the authors' recent $\epsilon$-expansion results [{\it Phys. Rev. B} {\bf 62} (2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case of an $m$-axial Lifshitz point. It is shown that the expansions obtained here by a direct calculation for the isotropic ($m=d$) Lifshitz point all follow from the latter upon setting $m=8-\epsilon_8$. This is so despite recent claims to the contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].Comment: 11 pages, Latex, uses iop stylefiles, some graphs are generated automatically via texdra

Numerical simulations of two dimensional magnetic domain patterns

I show that a model for the interaction of magnetic domains that includes a short range ferromagnetic and a long range dipolar anti-ferromagnetic interaction reproduces very well many characteristic features of two-dimensional magnetic domain patterns. In particular bubble and stripe phases are obtained, along with polygonal and labyrinthine morphologies. In addition, two puzzling phenomena, namely the so called `memory effect' and the `topological melting' observed experimentally are also qualitatively described. Very similar phenomenology is found in the case in which the model is changed to be represented by the Swift-Hohenberg equation driven by an external orienting field.Comment: 8 pages, 8 figures. Version to appear in Phys. Rev.

Finite Size Effects in Thermal Field Theory

We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary surfaces (two parallel hyperplanes), which break translational symmetry. In order to identify the singular parts of the one-loop two-point and four-point Schwinger functions, we use a combination of dimensional and zeta-function analytic regularization procedures. The infinities which occur in both the regularized one-loop two-point and four-point Schwinger functions fall into two distinct classes: local divergences that could be renormalized with the introduction of the usual bulk counterterms, and surface divergences that demand countertems concentrated on the boundaries. We present the detailed form of the surface divergences and discuss different strategies that one can assume to solve the problem of the surface divergences. We also briefly mention how to overcome the difficulties generated by infrared divergences in the case of Neumann-Neumann boundary conditions.Comment: 31 pages, latex, to appear in J. Math. Phy

Risk factors associated with Toxoplasma gondii infection in dairy cattle, State of Rio de Janeiro.

Toxoplasmosis is one of the most common parasitic zoonoses throughout the world. Infection in man and animals varies in different geographical areas influenced by many environmental conditions. Seroprevalence of Toxoplasma gondii infection in cattle in Brazil ranges from 1.03 to 71%. A cross-sectional survey was carried out in 58 out of 453 farms in the South Fluminense Paraiba Valley, State of Rio de Janeiro, Brazil. Over 3-year-old cattle (n=589) from dairy herds were selected for blood collection and detection of anti-T. gondii antibodies by indirect immunofluorescence reaction (IFA) with initial titration of 1:16; titers ? 64 were considered positive. Univariate analysis of risk factors showed that cats in contact with cattle, cats in contact with drinking water, and number of cats were associated with T. gondii seroprevalence. Logistic regression revealed a two-fold increased risk for infection of cattle (p=0.0138) through larger number of cats (>3) compared with low numbers of cats (1-2) on the farm. In contrast, the presence of chickens was considered a protective factor (p=0.025). Toxoplasmose é uma das mais comuns zoonoses parasitárias do mundo. Infecções em seres humanos e em animais variam nas diferentes áreas geográficas influenciadas pelas condições ambientais. A soroprevalência da infecção por Toxoplasma gondii em bovinos no Brasil varia de 1,03 a 71,0%. O estudo transversal foi realizado em 58 de um total de 453 propriedades na região Sul Fluminense do estado do Rio de Janeiro. Vacas leiteiras acima de 3 anos de idade (n=589) foram selecionadas para coleta de sangue e a detecção de anticorpos anti-T. gondii foi feita pelo teste de imunofluorescência indireta (IFI) com titulação inicial de 1:16 e títulos ? 64 foram considerados positivos. Após análise univariada dos fatores de risco, gatos em contato com bovinos, em contato com a água de beber dos animais e o número de gatos foram associados com a soroprevalência de T. gondii. A regressão logística demonstrou que o número maior de gatos (>3) teve um risco duas vezes maior (p=0,0138) que propriedades que tinham um número menor de gatos (1-2). Em contraste, a presença de galinhas foi considerada um fator de proteção (p=0,025)

A new picture of the Lifshitz critical behavior

New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8) situations. The general theory is illustrated for the N-vector phi^4 model describing a d-dimensional system. A new regularization and renormalization procedure is presented for both types of Lifshitz behavior. The anisotropic cases are formulated with two independent renormalization group transformations. The description of the isotropic behavior requires only one type of renormalization group transformation. We point out the conceptual advantages implicit in this picture and show how this framework is related to other previous renormalization group treatments for the Lifshitz problem. The Feynman diagrams of arbitrary loop-order can be performed analytically provided these integrals are considered to be homogeneous functions of the external momenta scales. The anisotropic universality class (N,d,m) reduces easily to the Ising-like (N,d) when m=0. We show that the isotropic universality class (N,m) when m is close to 8 cannot be obtained from the anisotropic one in the limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in good agreement with recent Monte Carlo simulations for the ANNNI model.Comment: 48 pages, no figures, two typos fixe

Yang-Lee Zeros of the Two- and Three-State Potts Model Defined on ϕ3\phi^3 Feynman Diagrams

We present both analytic and numerical results on the position of the partition function zeros on the complex magnetic field plane of the $q=2$ (Ising) and $q=3$ states Potts model defined on $\phi^3$ Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the $q=3$ states Potts model our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.Comment: 16 pages, 2 figures. Third version: the title was slightly changed. To be published in Physical Review