Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0

We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the three-dimensional N-vector universality class for N=0. We obtain g* = 1.4005(5), where g is normalized so that the three-dimensional field-theoretical beta-function behaves as \beta(g) = - g + g^2 for small g. As a byproduct, we also obtain precise estimates of the interpenetration ratio Psi*, Psi* = 0.24685(11), and of the exponent \nu, \nu = 0.5876(2).Comment: 16 page

Form factor expansion of the row and diagonal correlation functions of the two dimensional Ising model

We derive and prove exponential and form factor expansions of the row correlation function and the diagonal correlation function of the two dimensional Ising model

Extended Scaling for the high dimension and square lattice Ising Ferromagnets

In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range above the critical temperature T_c, with the scaling variable tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent effective exponents can be defined over all T using the same expressions. For the canonical two dimensional square lattice Ising ferromagnet it is shown that compact "extended scaling" expressions analogous to the high dimensional limit forms give accurate approximations to the true temperature dependencies, again over the entire temperature range from T_c to infinity. Within this approach there is no cross-over temperature in finite dimensions above which mean-field-like behavior sets in.Comment: 6 pages, 6 figure

Critical behaviour of the two-dimensional Ising susceptibility

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hundred terms, generated in about 100 hours on an obsolete workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2. To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4} singularity contains only integer powers of \tau. The presence of irrelevant variables in the scaling function is clearly evident, with contributions of distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being identified.Comment: 11 pages, REVTex

Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point

We compute the non--trivial infrared $\phi^4_3$--fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum space renormalization group. We choose a coordinate representation for the fixed point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponent $\nu$ up to order twenty five of interpolation expansion in this representation, and evaluate it using \pade, Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The resummation returns $0.6262(13)$ as the value of $\nu$.Comment: 29 pages, Latex2e, 2 Postscript figure

Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation

The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop approximation and the RG series obtained are resummed using the Borel-Leroy transformation combined with the generalized Pad\'e approximant and conformal mapping techniques. For the cubic model, the RG flows for various N are investigated. For N=2 it is found that the continuous line of fixed points running from the XY fixed point to the Ising one is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta functions closer to each another. For the cubic model with N\geq 3, the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N>2 is an artifact of the perturbative analysis. For the quenched dilute O(M) models ($MN$ models with N=0) the results are compatible with a stable pure fixed point for M\geq1. For the MN model with M,N\geq2 all the non-perturbative results are reproduced. In addition a new stable fixed point is found for moderate values of M and N.Comment: 26 pages, 3 figure

Addendum-erratum to: ``Nonasymptotic critical behavior from field theory at d=3. II. The ordered-phase case. Phys. Rev. B35, 3585 (1987)

This note is intended to emphasize the existence of estimated Feynman integrals in three dimensions for the free energy of the O(1) scalar theory up to five loops which may be useful for other work. We also correct some misprints of the published paper.Comment: One figure and one table added, some additions in the tex

Viroses e sua importância na viticultura brasileira.

A videira (Vitis spp.) é afetada por inúmeras viroses e muitas constituem causas da baixa produtividade e da perda de qualidade da uva. Das viroses de importância para a viticultura mundial, já foram identificadas no Brasil quatro de maior relevância: enrolamento da folha (leafroll), intumescimento dos ramos (corky bark), caneluras do tronco (stem grooving, stem pitting) e degenerescência da videira (janleaf); e duas de menor relevância econômica que ocorrem de forma latente na maioria das cultivares: necrose das nervuras (vein necrosis) e manchas das nervuras (jleck). No presente trabalho, é feito um breve relato sobre estas doenças, abrangendo incidência, danos, etiologia, sintomatologia, epidemiologia, diagnose e controle. Palavras-chave: Diagnose; Seleção sanitária; Termoterapia; Vitis spp

Low temperature series expansions for the square lattice Ising model with spin S > 1

We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We determine the location of the physical critical point and non-physical singularities. The number of non-physical singularities closer to the origin than the physical critical point grows quite rapidly with $S$. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of $S$. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of $S$, though consistent with universality.Comment: 14 pages, LaTeX with IOP style files (ioplppt.sty), epic.sty and eepic.sty. To appear in J. Phys.

Singularities of nn-fold integrals of the Ising class and the theory of elliptic curves

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for $n=1, 2, 3, 4$ and only modulo some primes for $n=5$ and $6$, thus providing a large set of (possible) new singularities of the $\chi^{(n)}$. We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to $n= 6$) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a {\em finite number of one dimensional integrals}. Among the singularities found, we underline the fact that the quadratic polynomial condition $1+3 w +4 w^2 = 0$, that occurs in the linear differential equation of $\chi^{(3)}$, actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure