Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the PT-symmetry of odd potentials for imaginary coupling parameter, and of generalized quantization conditions which take into account instanton contributions. We find a number of explicit new results, including the general behaviour of large-order perturbation theory for arbitrary levels of odd anharmonic oscillators, and subleading corrections to the decay width of excited states for odd potentials, which are numerically significant.Comment: 5 pages, RevTe

Imaginary Cubic Perturbation: Numerical and Analytic Study

The analytic properties of the ground state resonance energy E(g) of the cubic potential are investigated as a function of the complex coupling parameter g. We explicitly show that it is possible to analytically continue E(g) by means of a resummed strong coupling expansion, to the second sheet of the Riemann surface, and we observe a merging of resonance and antiresonance eigenvalues at a critical point along the line arg(g) = 5 pi/4. In addition, we investigate the convergence of the resummed weak-coupling expansion in the strong coupling regime, by means of various modifications of order-dependent mappings (ODM), that take special properties of the cubic potential into account. The various ODM are adapted to different regimes of the coupling constant. We also determine a large number of terms of the strong coupling expansion by resumming the weak-coupling expansion using the ODM, demonstrating the interpolation between the two regimes made possible by this summation method.Comment: 18 pages; 4 figures; typographical errors correcte

Self-Consistent Theory of Normal-to-Superconducting Transition

I study the normal-to-superconducting (NS) transition within the Ginzburg-Landau (GL) model, taking into account the fluctuations in the $m$-component complex order parameter \psi\a and the vector potential $\vec A$ in the arbitrary dimension $d$, for any $m$. I find that the transition is of second-order and that the previous conclusion of the fluctuation-driven first-order transition is an artifact of the breakdown of the \eps-expansion and the inaccuracy of the $1/m$-expansion for physical values \eps=1, $m=1$. I compute the anomalous $\eta(d,m)$ exponent at the NS transition, and find $\eta (3,1)\approx-0.38$. In the $m\to\infty$ limit, $\eta(d,m)$ becomes exact and agrees with the $1/m$-expansion. Near $d=4$ the theory is also in good agreement with the perturbative \eps-expansion results for $m>183$ and provides a sensible interpolation formula for arbitrary $d$ and $m$.Comment: 9 pages, TeX + harvmac.tex (included), 2 figures and hard copies are available from [email protected] To appear in Europhysics Letters, January, 199

Higher-Order Corrections to Instantons

The energy levels of the double-well potential receive, beyond perturbation theory, contributions which are non-analytic in the coupling strength; these are related to instanton effects. For example, the separation between the energies of odd- and even-parity states is given at leading order by the one-instanton contribution. However to determine the energies more accurately multi-instanton configurations have also to be taken into account. We investigate here the two-instanton contributions. First we calculate analytically higher-order corrections to multi-instanton effects. We then verify that the difference betweeen numerically determined energy eigenvalues, and the generalized Borel sum of the perturbation series can be described to very high accuracy by two-instanton contributions. We also calculate higher-order corrections to the leading factorial growth of the perturbative coefficients and show that these are consistent with analytic results for the two-instanton effect and with exact data for the first 200 perturbative coefficients.Comment: 7 pages, LaTe

Influence of quark boundary conditions on the pion mass in finite volume

We calculate the mass shift for the pion in a finite volume with renormalization group (RG) methods in the framework of the quark-mesons model. In particular, we investigate the importance of the quark effects on the pion mass. As in lattice gauge theory, the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes, in addition to the shift due to pion interactions. We compare our results to chiral perturbation theory calculations and find differences due to the fact that chiral perturbation theory only considers pion effects in the finite volume.Comment: 24 pages, 5 figures, RevTex4, published version, discussion of lattice results extende

Two-loop beta functions of the Sine-Gordon model

We recalculate the two-loop beta functions in the two-dimensional Sine-Gordon model in a two-parameter expansion around the asymptotically free point. Our results agree with those of Amit et al., J. Phys. A13 (1980) 585.Comment: 6 pages, LaTeX, some correction

Absence of vortex condensation in a two dimensional fermionic XY model

Motivated by a puzzle in the study of two dimensional lattice Quantum Electrodynamics with staggered fermions, we construct a two dimensional fermionic model with a global U(1) symmetry. Our model can be mapped into a model of closed packed dimers and plaquettes. Although the model has the same symmetries as the XY model, we show numerically that the model lacks the well known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing the absence of a phase with vortex condensation. In other words the low energy physics is described by a non-compact U(1) field theory. We show that by introducing an even number of layers one can introduce vortex condensation within the model and thus also induce a KT transition.Comment: 5 pages, 5 figure

Conformal invariance in three-dimensional rotating turbulence

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.Comment: 4 pages, 3 figures, submitted to PR

Modeling pion physics in the ϵ\epsilon-regime of two-flavor QCD using strong coupling lattice QED

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with U(1) gauge fields. For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times U_A(1)$ symmetry. By adding a four-fermion term we can break the U_A(1) symmetry and thus incorporate the physics of the QCD anomaly. We can also tune the pion decay constant F, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy pion physics in a setting similar to lattice QCD from first principles. However, unlike lattice QCD, a major advantage of our model is that we can easily design efficient algorithms to compute a variety of quantities in the chiral limit. Here we show that the model reproduces the predictions of chiral perturbation theory in the $\epsilon$-regime.Comment: 24 pages, 7 figure

Multifractality in a broad class of disordered systems

We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold. Each of the cumulants has its own independent critical exponent, i.e., there are infinitely many critical exponents involved in the problem. Working out the connection to the random resistor network, we determine these multifractal exponents to two-loop order. Depending on the specifics of the Hamiltonian of each individual model, the amplitudes of the higher cumulants can vanish and in this case, effectively, only some of the multifractal exponents are required.Comment: 4 pages, 1 figur