Finite size analysis of the pseudo specific heat in SU(2) gauge theory

We investigate the pseudo specific heat of SU(2) gauge theory near the crossover point on $4^4$ to $16^4$ lattices. Several different methods are used to determine the specific heat. The curious finite size dependence of the peak maximum is explained from the interplay of the crossover phenomenon with the deconfinement transition occurring due to the finite extension of the lattice. In this context we calculate the modulus of the lattice average of the Polyakov loop on symmetric lattices and compare it to the prediction from a random walk model.Comment: Talk presented at LATTICE96(finite temperature), 3 pages, 4 Postscript figure

The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence and Finite Temperature Effects

We investigate the pseudo specific heat of SU(2) gauge theory near the crossover point on $4^4$ to $16^4$ lattices. Several different methods are used to determine the specific heat. The curious finite size dependence of the peak maximum is explained from the interplay of the crossover phenomenon with the deconfinement transition occurring due to the finite extension of the lattice. We find, that for lattices of size $8^4$ and larger the crossover peak is independent of lattice size at $\beta_{co}=2.23(2)$ and has a peak height of $C_{V,co}=1.685(10)$. We conclude therefore that the crossover peak is not the result of an ordinary phase transition. Further, the contributions to $C_V$ from different plaquette correlations are calculated. We find, that at the peak and far outside the peak the ratio of contributions from orthogonal and parallel plaquette correlations is different. To estimate the finite temperature influence on symmetric lattices far off the deconfinement transition point we calculate the modulus of the lattice average of the Polyakov loop on these lattices and compare it to predictions from a random walk model.Comment: Latex 2e,10 pages including 5 postscript figure

Corrections to Scaling and Critical Amplitudes in SU(2) Lattice Gauge Theory

We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of SU(2) gauge theory. To this end we carefully study the corrections to the scaling functions of the observables coming from irrelevant exponents. As a guiding line for determining the critical amplitudes we use envelope equations derived from the finite size scaling formulae for the observables. The equations are then evaluated with new high precision data obtained on N^3 x 4 lattices for N=12,18,26 and 36. We find different correction-to-scaling behaviours above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C_+/C_-=4.72(11) and agrees perfectly with a recent measurement for the 3d Ising model.Comment: LATTICE98(hightemp

Direct determination of the gauge coupling derivatives for the energy density in lattice QCD

By matching Wilson loop ratios on anisotropic lattices we measure the coefficients \cs and \ct, which are required for the calculation of the energy density. The results are compared to that of an indirect method of determination. We find similar behaviour, the differences are attributed to different discretization errors.Comment: Talk presented at LATTICE97(finite temperature), 3 pages, 5 Postscript figure

A Study of Finite Temperature Gauge Theory in (2+1) Dimensions

We determine the critical couplings and the critical exponents of the finite temperature transition in SU(2) and SU(3) pure gauge theory in (2+1) dimensions. We also measure Wilson loops at $T=0$ on a wide range of $\beta$ values using APE smearing to improve the signal. We extract the string tension $\sigma$ from a fit to large distances, including a string fluctuation term. With these two entities we calculate $T_c/\sqrt{\sigma}$.Comment: Talk presented at LATTICE96(finite temperature), not espcrc2 style: 7 pages, 4 ps figures, 22 k

The string tension in SU(N) gauge theory from a careful analysis of smearing parameters

We report a method to select optimal smearing parameters before production runs and discuss the advantages of this selection for the determination of the string tension.Comment: Contribution to Lat97 poster session, title was 'How to measure the string tension', 3 pages, 5 colour eps figure

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

The Calculation of Critical Amplitudes in SU(2) Lattice Gauge Theory

We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of (3+1) dimensional SU(2) gauge theory. To this end we study the corrections due to irrelevant exponents in the scaling functions. As a guiding line for determining the critical amplitudes we use envelope equations which we derive from the finite size scaling formulae of the observables. We have produced new high precision data on N^3 x 4 lattices for N=12,18,26 and 36. With these data we find different corrections to the asymptotic scaling behaviour above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C_+/C_-=4.72(11) and thus in excellent agreement with a recent measurement for the 3d Ising model.Comment: 27 pages, 11 figures, Latex2

Self-stabilizing Overlays for high-dimensional Monotonic Searchability

We extend the concept of monotonic searchability for self-stabilizing systems from one to multiple dimensions. A system is self-stabilizing if it can recover to a legitimate state from any initial illegal state. These kind of systems are most often used in distributed applications. Monotonic searchability provides guarantees when searching for nodes while the recovery process is going on. More precisely, if a search request started at some node $u$ succeeds in reaching its destination $v$, then all future search requests from $u$ to $v$ succeed as well. Although there already exists a self-stabilizing protocol for a two-dimensional topology and an universal approach for monotonic searchability, it is not clear how both of these concepts fit together effectively. The latter concept even comes with some restrictive assumptions on messages, which is not the case for our protocol. We propose a simple novel protocol for a self-stabilizing two-dimensional quadtree that satisfies monotonic searchability. Our protocol can easily be extended to higher dimensions and offers routing in $\mathcal O(\log n)$ hops for any search request