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

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.

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

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

New results for the t-J model in ladders: Changes in the spin liquid state with applied magnetic field. Implications for the cuprates

Exact Diagonalization calculations are presented for the t-J model in the presence of a uniform magnetic field. Results for 2xL ladders (L=8,10,12) and 4x4 square clusters with 1 and 2 holes indicate that the diamagnetic response to a perpendicular magnetic field tends to induce a spin liquid state in the spin background. The zero-field spin liquid state of a two-leg ladder is reinforced by the magnetic field: a considerable increase of rung antiferromagnetic correlations is observed for J/t up to 0.6, for 1 and 2 holes. Pair-breaking is also clearly observed in the ladders and seems to be associated in part with changes promoted by the field in the spin correlations around the zero-field pair. In the 4x4 cluster, the numerical results seem to indicate that the field-induced spin liquid state competes with the zero-field antiferromagnetic short-range-order, the spin liquid state being favored by higher doping and smaller values of J/t. It is interesting to note that the field-effect can also be observed in a 2x2 plaquette with 1 and 2 holes. This opens up the possibility of gaining a qualitative understanding of the effect.Comment: 16 pages, 7 figures, latex New results adde