arXiv subjects

C. B. Lang

Publications and source records attributed to C. B. Lang.

144 records · Page 8Linked to original sources

arXiv1996

Non-Gaussian fixed point candidates in the 4D compact U(1) gauge theories

Some interesting nonperturbative properties of the strongly coupled 4D compact U(1) lattice gauge theories, both without and with matter fields, are pointed out. We demonstrate that the pure gauge theory has a non-Gaussian fixed point with $ν= 0.365(8)$ at the second order confinement-Coulomb phase transition. Thus a non-asymptotic free and nontrivial continuum limit of this theory, and of its various dual equivalents, in particular of a special case of the effective string theory, can be constructed. Including a scalar matter field (compact scalar QED), we confirm the Gaussian behavior at the endpoint of the Higgs phase transition line. In the theory with both scalar and fermion matter fields, we demonstrate the existence of a tricritical point. Here, the chiral symmetry is broken, and the mass of unconfined composite fermions is generated dynamically. Appart from the Goldstone bosons, the spectrum contains also a massive scalar. This resembles the Higgs-Yukawa sector of the SM, albeit of dynamical origin, like the Nambu--Jona-Lasinio model. However, the scaling behavior is different from that in the NJL model and the nonperturbative renormalizability might thus be possible.

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arXiv1996

Four-dimensional pure compact U(1) gauge theory on a spherical lattice

We investigate the confinement-Coulomb phase transition in the four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The action contains the Wilson coupling beta and the double charge coupling gamma. The lattice is obtained from the 4D surface of the 5D cubic lattice by its radial projection onto a 4D sphere, and made homogeneous by means of appropriate weight factors for individual plaquette contributions to the action. On such lattices the two-state signal, impeding the studies of this theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a consistent finite-size scaling behavior of several bulk observables is found, with the correlation length exponent nu in the range nu = 0.35 - 40. These observables include Fisher zeros, specific-heat and cumulant extrema as well as pseudocritical values of beta at fixed gamma. The most reliable determination of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at gamma le 0 is thus very probably of 2nd order and belongs to the universality class of a non-Gaussian fixed point.

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arXiv1996

Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice

The line of phase transitions, separating the confinement and the Coulomb phases in the four-dimensional pure compact U(1) gauge theory with extended Wilson action, is reconsidered. We present new numerical evidence that a part of this line, including the original Wilson action, is of second order. By means of a high precision simulation on homogeneous lattices on a sphere we find that along this line the scaling behavior is determined by one fixed point with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the existence of a nontrivial and nonasymptotically free four-dimensional pure U(1) gauge theory in the continuum very probable. The universality and duality arguments suggest that this conclusion holds also for the monopole loop gas, for the noncompact abelian Higgs model at large negative squared bare mass, and for the corresponding effective string theory.

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arXiv1996

Universality of the Ising Model on Sphere-like Lattices

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes ranging up to O($10^5$) sites are simulated and finite size scaling is analyzed. The partition function zeros and the values of various cumulants at their respective peak positions are determined and they agree with the scaling behavior expected from universality with the Onsager solution on the torus ($ν=1$). For the pseudocritical values of the coupling we find significant anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice topology.

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arXiv1995

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 $ν\simeq 0.36(1)$.

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arXiv1995

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 $ν=1$, in the universality class of the Ising model or, equivalently, the lattice model of free fermions.

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arXiv1994

Evidence for a Critical Behavior in $4D$ 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 $γ$.

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arXiv1994

Lee-Yang zeroes in the one flavour massive lattice Schwinger model

We study the partition function of the model formulated with Wilson fermions with only one species, both analytically and numerically. At strong coupling we construct the solution for lattice size up to $8\times 8$, a polynomial in the hopping parameter up to $O(\ka^{128})$. At $\be>0$ we evaluate the expectation value of the fermion determinant for complex values of $\ka$. From the Lee-Yang zeroes we find support for the existence of a line of phase transitions from $(\be=0, \ka\simeq 0.38)$ up to $(\be=\infty, \ka=1/4)$.

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arXiv1994

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.

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arXiv1993

Computer Stochastics in Scalar Quantum Field Theory

This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point properties and logarithmic corrections, partition function zeroes, the triviality bound on the Higgs mass, finite size effects, Goldstone bosons and chiral perturbation theory, and the determination of scattering phase shifts for some scalar models.

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arXiv1993

The First Order Signal in Pure U(1) Gauge Theory May be Fake

We study the deconfinement phase transition of compact $U(1)$ pure lattice gauge theory with the Wilson action on {\em closed topology} lattices. In contrast to studies of compact QED on {\em hypercubic lattices with periodic boundary conditions}, we find no metastability signal at the phase transition on the lattices with the topology of a sphere. Thus the determination of the order of this phase transition has to be reconsidered. We argue that different properties of closed monopole loops on these topological inequivalent lattices might be responsible for the effect.

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arXiv1993

Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model

The scaling behaviour of the edge of the Lee--Yang zeroes in the four dimensional Ising model is analyzed. This model is believed to belong to the same universality class as the $ϕ^4_4$ model which plays a central role in relativistic quantum field theory. While in the thermodynamic limit the scaling of the Yang--Lee edge is not modified by multiplicative logarithmic corrections, such corrections are manifest in the corresponding finite--size formulae. The asymptotic form for the density of zeroes which recovers the scaling behaviour of the susceptibility and the specific heat in the thermodynamic limit is found to exhibit logarithmic corrections too. The density of zeroes for a finite--size system is examined both analytically and numerically.

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arXiv1993

On the Phase Structure of the Schwinger Model with Wilson Fermions

We study the phase structure of the massive one flavour lattice Schwinger model on the basis of the finite size scaling behaviour of the partition function zeroes. At $β= 0$ we observe and discuss a possible discrepancy with results obtained by a different method.

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arXiv1992

Scattering in a Simple 2-d Lattice Model

Lüscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass and coupled through a 3-point term, both considered in the symmetric phase. The Monte Carlo simulation makes use of the cluster updating and reduced variance operator techniques. For the Ising system we study in particular O($a^2$) effects in the phase shift of the 2-particle scattering process.

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arXiv1992

Lee-Yang Zeroes and Logarithmic Corrections in the $Φ^4_4$ Theory

The leading mean-field critical behaviour of $ϕ^4_4$-theory is modified by multiplicative logarithmic corrections. We analyse these corrections both analytically and numerically. In particular we present a finite-size scaling theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit logarithmic corrections. On lattices from size $8^4$ to $24^4$, Monte-Carlo cluster methods and multi-histogram techniques are used to determine the partition function zeroes closest to the critical point. Finite-size scaling behaviour is verified and the logarithmic corrections are found to be in good agreement with our analytical predictions.

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arXiv1992

Renormalization Group Analysis of Finite-Size Scaling in the $Φ^4_4$ Model

A finite-size scaling theory for the $ϕ^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the leading scaling behaviour is identical to that of mean field theory, there exist multiplicative logarithmic corrections too. A non-perturbative test of these formulae in the form of a high precision Monte Carlo analysis reveals good quantitative agreement with the analytical predictions.

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arXiv1992

Rotational Symmetry and Regularization Dependence in the $Φ^4_4$-Model

We study the one component $Φ^4$ model for four different lattice actions in the Gaussian limit and for the Ising model in the broken phase. Emphasis is put on the euclidean invariance properties of the boson propagator. A measure of the violation of rotational symmetry serves as a tool to compare the regularization dependence of the triviality bound.

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arXiv1992

Resonance Scattering Phase Shifts in a 2-d Lattice Model

We study a simple 2-d model representing two fields with different mass and a 3-point coupling term. The phase shift in the resonating 2-particle channel is determined from the energy spectrum obtained in Monte Carlo simulations on finite lattices. Masses and wave function renormalization constants of the fields as well as mass and width of the resonance are determined and discussed. The representation of scattering states in terms of the considered operators is analysed.

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