Evidence for a Critical Behavior in 4D4D Pure Compact QED

We present evidence about a critical behavior of $4D$ compact QED (CQED) pure gauge theory. Regularizing the theory on lattices homotopic to a sphere, we present evidence for a critical, i.e. second order like behavior at the deconfinement phase transition for certain values of the coupling parameter $\gamma$.Comment: 3 pages, 3 figures, POSTSCRIPT file (127KB uuencoded

A fixed-point action for the lattice Schwinger model

We determine non-perturbatively a fixed-point (FP) action for fermions in the two-dimensional U(1) gauge (Schwinger) model. Our parameterization for the fermionic action has terms within a $7\times 7$ square on the lattice, using compact link variables. With the Wilson fermion action as starting point we determine the FP-action by iterating a block spin transformation (BST) with a blocking factor of 2 in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. We simulate the model at various values of $\beta$ and find excellent improvement for the studied observables.Comment: 3 pages (LaTeX), 2 figures (EPS

Chiral symmetry in the 2-flavour lattice Schwinger model

We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion species of identical mass. In the simulation we are using Wilson fermions where chiral symmetry is explicitly broken. Since there is no known simple order parameter it is non-trivial to identify the critical line of the chiral phase transition. We therefore need to find observables which allow an identification of a possible restoration of chiral symmetry. We utilize the PCAC-relations in order to identify the critical coupling, where chiral symmetry is restored.Comment: 3 pages (LaTeX), 4 figures (EPS

Spin and Gauge Systems on Spherical Lattices

We present results for 2D and 4D systems on lattices with topology homotopic to the surface of a (hyper) sphere $S^2$ or $S^4$. Finite size scaling is studied in situations with phase transitions of first and second order type. The Ising and Potts models exhibit the expected behaviour; for the 4D pure gauge $U(1)$ theory we find consistent scaling indicative of a second order phase transition with critical exponent $\nu\simeq 0.36(1)$.Comment: 4 pages, LaTeX, 3 POSTSCRIPT figures (uuencoded

Chiral properties of the fixed point action of the Schwinger model

We study the spectrum properties for a recently constructed fixed point lattice Dirac operator. We also consider the problem of the extraction of the fermion condensate, both by direct computation, and through the Banks-Casher formula by analyzing the density of eigenvalues of a redefined antihermitean lattice Dirac operator.Comment: 14 pages (LaTeX), 4 figures (EPS

U(1) Gauge Theory with Villain Action on Spherical Lattices

We have studied the U(1) gauge field theory with Villain (periodic Gaussian) action on spherelike lattices. The effective size of the systems studied ranges from 6 to 16. We do not observe any 2-state signal in the distribution function of the plaquette expectation value at the deconfining phase transition. The observed finite-size scaling behavior is consistent with a second order phase transition. The obtained value of the critical exponent is nu =0.366(12) and thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a nontrivial continuum limit.Comment: 10 pages, LaTeX, 2 figure

Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory

We investigate the scaling behaviour of gauge-ball masses and static potential in the pure U(1) lattice gauge theory on toroidal lattices. An extended gauge field action $-\sum_P(\beta \cos\Theta_P + \gamma \cos2\Theta_P)$ is used with $\gamma= -0.2$ and -0.5. Gauge-ball correlation functions with all possible lattice quantum numbers are calculated. Most gauge-ball masses scale with the non-Gaussian exponent $\nu_{ng}\approx 0.36$. The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $\nu_{g} \approx 0.5$ in the investigated range of correlation lengths. The static potential is examined with Sommer's method. The long range part scales consistently with $\nu_{ng}$ but the short range part tends to yield smaller values of $\nu$. The $\beta$-function, having a UV stable zero, is obtained from the running coupling. These results hold for both $\gamma$ values, supporting universality. Consequences for the continuum limit of the theory are discussed.Comment: Contribution to the Lattice 97 proceedings, LaTeX, 3 pages, 3 figure

Properties of the non-Gaussian fixed point in 4D compact U(1) lattice gauge theory

We examine selected properties of the gauge-ball spectrum and fermionic variables in the vicinity of the recently discussed non-Gaussian fixed point of 4D compact U(1) lattice gauge theory within the quenched approximation. Approaching the critical point from within the confinement phase, our data support scaling of $T1^{+-}$ gauge-ball states in units of the string tension square root. The analysis of the chiral condensate within the framework of a scaling form for the equation of state suggests non mean-field values for the magnetic exponents $\delta$ and $\beta_{exp}$.Comment: 73K postscript fil

Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

We study the pure gauge model on a lattice manifold with trivial fundamental homotopy group, homotopically equivalent to an $S_4$. Monopole loops may fluctuate freely on that lattice without restrictions due to the boundary conditions. For the original Wilson action on the hypertorus there is an established two-state signal in energy distribution functions which disappears for the new geometry. Our finite size scaling analysis suggests stringent upper bounds on possible discontinuities in the plaquette action. However, no consistent asymptotic finite size scaling behaviour is observed.Comment: 18 pages (3 figures), LaTeX + POSTSCRIPT (287 KB), preprint BI-TP 94/3

Strong Coupling Lattice Schwinger Model on Large Spherelike Lattices

The lattice regularized Schwinger model for one fermion flavor and in the strong coupling limit is studied through its equivalent representation as a restricted 8-vertex model. The Monte Carlo simulation on lattices with torus-topology is handicapped by a severe non-ergodicity of the updating algorithm; introducing lattices with spherelike topology avoids this problem. We present a large scale study leading to the identification of a critical point with critical exponent $\nu=1$, in the universality class of the Ising model or, equivalently, the lattice model of free fermions.Comment: 16 pages + 7 figures, gzipped POSTSCRIPT fil