Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD

We calculate numerically universal finite-size-scaling functions of the magnetization for the three-dimensional O(4) and O(2) spin models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.Comment: Lattice2001(hightemp), 3 pages, 5 figures, acknowledgements completed, minor typographical errors correcte

Block Spin Effective Action for Polyakov Loops in 4D SU(2) LGT

Using a variant of the IMCRG method of Gupta and Cordery, we explicitly compute majority rule block spin effective actions for the signs of the Polyakov loops in 4D SU(2) finite temperature lattice gauge theories. To the best of our knowledge, this is the first attempt to compute numerically effective actions for the Polyakov loop degrees of freedom in 4D SU(2). The most important observations are: 1. The renormalization group flow at the deconfinement transition can be nicely matched with the flow of the 3D Ising model, thus confirming the Svetitsky-Yaffe conjecture. 2. The IMCRG simulations of the FT SU(2) model have strongly reduced critical slowing down.Comment: Contribution to the Lattice 97 proceedings, LaTeX, 3 pages, 3 figures, uses espcrc2.sty, epsfig.st

Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the χ2\chi^2-method

We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$ of critical exponents of the deconfinement transition in $SU(2)$ gauge theory by applying the $\chi^2$-method to Monte Carlo data of the modulus and the square of the Polyakov loop. With the same technique we find from the Binder cumulant $g_r$ its universal value at the critical point in the thermodynamical limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in complete agreement with that of the $3d$ Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te

Specific heat and energy for the three-dimensional O(2) model

We investigate the three-dimensional O(2) model on lattices of size 8^3 to 160^3 close to the critical point at zero magnetic field. We confirm explicitly the value of the critical coupling J_c found by Ballesteros et al. and estimate there the universal values of g_r and xi/L. At the critical point we study the finite size dependencies of the energy density epsilon and the specific heat C. We find that the nonsingular part of the specific heat C_{ns} is linearly dependent on 1/alpha. From the critical behaviour of the specific heat for T not T_c on the largest lattices we determine the universal amplitude ratio A+/A-. The alpha- dependence of this ratio is close to the phenomenological relation A+/A- = 1-4alpha.Comment: Lattice2001(spin), 3 pages, 4 figure

The chiral transition of N_f=2 QCD with fundamental and adjoint fermions

We study QCD with two staggered Dirac fermions both in the fundamental (QCD) and the adjoint representation (aQCD) near the chiral transition. The aim is to find the universality class of the chiral transition and to verify Goldstone effects below the transition. We investigate aQCD, because in that theory the deconfinement and the chiral transitions occur at different temperatures T_d<T_c. Here, we show that the scaling behaviour of the chiral condensate in the vicinity of \beta_c is in full agreeement with that of the 3d O(2) universality class. In the region T_d<T<T_c we confirm the quark mass dependence of the chiral condensate which is expected due to the existence of Goldstone modes like in 3d O(N) spin models. For fundamental QCD we use the p4-action. Here, we find Goldstone effects below T_c like in aQCD and the 3d O(N) spin models, however no O(2)/O(4) scaling near the chiral transition point. The result for QCD may be a consequence of the coincidence of the deconfinement transition with the chiral transition.Comment: 6 pages, 5 figures, poster contribution to Lattice 2005 (Nonzero temperature and density), one reference added, figure 2 change

Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks

We study QCD with two Dirac fermions in the adjoint representation at finite temperature by Monte Carlo simulations.In such a theory the deconfinement and chiral phase transitions occur at different temperatures. We locate the second order chiral transition point at beta_c=5.624(2) and show that the scaling behaviour of the chiral condensate in the vicinity of beta_c is in full agreeement with that of the 3d O(2) universality class, and to a smaller extent comparable to the 3d O(6) class. From the previously determined first order deconfinement transition point beta_d=5.236(3) and the two-loop beta function we find the ratio T_c/T_d = 7.8(2). In the region between the two phase transitions we explicitly confirm the quark mass dependence of the chiral condensate which is expected due to the existence of Goldstone modes like in 3d O(N) spin models. At the deconfinement transition the condensate shows a gap, and below beta_d, it is nearly mass-independent for fixed beta.Comment: 28 pages, 12 figures, Latex2

Non-perturbative determination of anisotropy coefficients and pressure gap at the deconfining transition of QCD

We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients). Our method is based on a precise measurement of the finite temperature deconfining transition curve in the lattice coupling parameter space extended to anisotropic lattices by applying the spectral density method. We determine the anisotropy coefficients for the cases of SU(2) and SU(3) gauge theories. A longstanding problem, when one uses the perturbative anisotropy coefficients, is a non-vanishing pressure gap at the deconfining transition point in the SU(3) gauge theory. Using our non-perturbative anisotropy coefficients, we find that this problem is completely resolved.Comment: LATTICE98(hightemp

A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model

We investigate numerically the three-dimensional O(2) model on 8^3-160^3 lattices as a function of the magnetic field H. In the low-temperature phase we verify the H-dependence of the magnetization M induced by the Goldstone modes and determine M in the thermodynamic limit on the coexistence line both by extrapolation and by chiral perturbation theory. We compute two critical amplitudes from the scaling behaviours on the coexistence line and on the critical line. In both cases we find negative corrections to scaling. With additional high temperature data we calculate the scaling function and show that it has a smaller slope than that of the O(4) model. For future tests of QCD lattice data we study as well finite-size-scaling functions.Comment: Lattice 2000 (Spin Models), minor typographic errors fixe

Back action of graphene charge detectors on graphene and carbon nanotube quantum dots

We report on devices based on graphene charge detectors (CDs) capacitively coupled to graphene and carbon nanotube quantum dots (QDs). We focus on back action effects of the CD on the probed QD. A strong influence of the bias voltage applied to the CD on the current through the QD is observed. Depending on the charge state of the QD the current through the QD can either strongly increase or completely reverse as a response to the applied voltage on the CD. To describe the observed behavior we employ two simple models based on single electron transport in QDs with asymmetrically broadened energy distributions of the source and the drain leads. The models successfully explain the back action effects. The extracted distribution broadening shows a linear dependency on the bias voltage applied to the CD. We discuss possible mechanisms mediating the energy transfer between the CD and QD and give an explanation for the origin of the observed asymmetry.Comment: 6 pages, 4 figure