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

Scaling of magnetic monopoles in the pure compact QED

In the pure U(1) lattice gauge theory with the Villain action we find that the monopole mass in the Coulomb phase and the monopole condensate in the confinement phase scale according to simple power laws. This holds outside the coupling region in which on finite toroidal lattices the metastability phenomena occur. A natural explanation of the observed accuracy of the scaling behaviour would be the second order of the phase transition between both phases in the general space of couplings not far away from the Villain action.Comment: LATTICE99(Topology and Confinement) - 3 pages, 4 fig

Study of the order of the phase transition in pure U(1) gauge theory with Villain action

We address the question of the order of the deconfinement phase transition of four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory dual to the Villain action on toroidal lattices up to lattice sizes of 28^4 give results consistent with both, a vanishing and a nonvanishing discontinuity in the thermodynamic limit. A decision on the order of the phase transition requires still larger lattice sizes.Comment: LATTICE98(gauge), 3 pages, 2 figure

Tricritical point in strongly coupled U(1) gauge theory with fermions and scalars

We investigate the tricritical point in the lattice fermion--gauge--scalar model with U(1) gauge symmetry. In the vicinity of this point, in the phase with the broken chiral symmetry, we observe the scaling behavior of the chiral condensate and of the masses of composite fermion and composite scalar, indicating the existence of an interesting continuum limit of the model at this point.Comment: Contribution to Lattice 95, LaTeX file (4 pages), 5 ps-figures appended (uuencoded

Magnetic and chiral universality classes in a 3D Yukawa model

The 3D Yukawa model with U(1) chiral symmetry is investigated in a broad interval of parameters using the Binder method. Critical exponents of the Wilson-Fisher (magnetic) and Gross-Neveu (chiral) universality classes are measured. The model is dominated by the chiral universality class. However at weak coupling we observe a crossover between both classes, manifested by difficulties with the Binder method which otherwise works well.Comment: 4 pages, contribution to LATTICE 9

Gauge invariant generalization of the 2D chiral Gross-Neveu model

By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu (GN$_2$) model to a U(1) gauge theory with charged fermion and scalar fields in 2D ($\chi U \phi_2$ model). The $\chi U \phi_2$ model is equivalent to the GN$_2$ model at infinite gauge coupling. We show that the dynamical fermion mass generation and asymptotic freedom in the effective four-fermion coupling persist also when the gauge coupling decreases. These phenomena are not influenced by the XY$_2$ model phase transition at weak coupling. This suggests that the $\chi U \phi_2$ model is in the same universality class as the GN$_2$ model and thus renormalizable.Comment: Contribution to Lattice 95, LaTeX file (4 pages), 4 ps-figures appended (uuencoded), abstract correcte

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

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

Strongly coupled compact lattice QED with staggered fermions

We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action -\sum_P [\beta \cos(\Theta_P) + \gamma \cos(2\Theta_P)], both for dynamical fermions and in the quenched approximation. (\Theta_P denotes the plaquette angle.) In simulations with dynamical fermions at various \gamma \le -0.2 on 6^4 lattices we find the energy gap at the phase transition of a size comparable to the pure gauge theory for \gamma \le 0 on the same lattice, diminishing with decreasing \gamma. This suggests a second order transition in the thermodynamic limit of the theory with fermions for \gamma below some finite negative value. Studying the theory on large lattices at \gamma = -0.2 in the quenched approximation by means of the equation of state we find non-Gaussian values of the critical exponents associated with the chiral condensate, \beta \simeq 0.32 and \delta \simeq 1.8, and determine the scaling function. Furthermore, we evaluate the meson spectrum and study the PCAC relation.Comment: 21 page

Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent $\nu \simeq 0.35$. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gauge-ball spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian value $\nu \simeq 0.5$. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.Comment: 46 pages, 12 figure