The nature of the continuum limit in strongly coupled quenched QED

We review the results of large scale simulations of noncompact quenched $QED$ which use spectrum and Equation of State calculations to determine the theory's phase diagram, critical indices, and continuum limit. The resulting anomalous dimensions are in good agreement with Schwinger-Dyson solutions of the ladder graphs of conventional $QED$ and they satisfy the hyperscaling relations expected of a relativistic renormalizable field theory. The spectroscopy results satisfy the constraints of the Goldstone mechanism and PCAC, and may be indicative of Technicolor versions of the Standard Model which are strongly coupled at short distances.Comment: (talk given at the XXVI ICHEP, Dallas, TX, Aug 6-12 92), 6 pp., ILL-(TH)-92-#2

On the Interplay of Monopoles and Chiral Symmetry Breaking in Non-Compact Lattice QED

Non-compact lattice QED is simulated for various numbers of fermion species $N_f$ ranging from 8 through 40 by the exact Hybrid Monte Carlo algorithm. Over this range of $N_f$, chiral symmetry breaking is found to be strongly correlated with the effective monopoles in the theory. For $N_f$ between 8 and 16 the chiral symmetry breaking and monopole percolation transitions are second order and coincident. Assuming powerlaw critical behavior, the correlation length exponent for the chiral transition is identical to that of monopole percolation. This result supports the conjecture that monopole percolation ``drives" the nontrivial chiral transition. For $N_f$ between 20 and 32, the monopoles experience a first order condensation transition coincident with a first order chiral transition. For $N_f$ as large as 40 both transitions are strongly suppressed. The data at large N_f (N_f \mathrel {\mathpalette \vereq >} 20) is interpreted in terms of a strongly interacting monopole gas-liquid transition.Comment: Revtex file, 23 pages, hardcopy figures only

Scaling functions for O(4) in three dimensions

Monte Carlo simulation using a cluster algorithm is used to compute the scaling part of the free energy for a three dimensional O(4) spin model. The results are relevant for analysis of lattice studies of high temperature QCD.Comment: 12 pages, 6 figures, uses epsf.st

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-\eta}$ at large volumes with $0\leq\eta\leq 0.25$ for $0\leq T\leq T_c$.Comment: Revtex format; 4 pages, 2 figure

On the Logarithmic Triviality of Scalar Quantum Electrodynamics

Using finite size scaling and histogram methods we obtain numerical results from lattice simulations indicating the logarithmic triviality of scalar quantum electrodynamics, even when the bare gauge coupling is chosen large. Simulations of the non-compact formulation of the lattice abelian Higgs model with fixed length scalar fields on $L^{4}$ lattices with $L$ ranging from $6$ through $20$ indicate a line of second order critical points. Fluctuation-induced first order transitions are ruled out. Runs of over ten million sweeps for each $L$ produce specific heat peaks which grow logarithmically with $L$ and whose critical couplings shift with $L$ picking out a correlation length exponent of $0.50(5)$ consistent with mean field theory. This behavior is qualitatively similar to that found in pure $\lambda\phi^{4}$.Comment: 9 page

Regularization-independent study of renormalized non-perturbative quenched QED

A recently proposed regularization-independent method is used for the first time to solve the renormalized fermion Schwinger-Dyson equation numerically in quenched QED$_4$. The Curtis-Pennington vertex is used to illustrate the technique and to facilitate comparison with previous calculations which used the alternative regularization schemes of modified ultraviolet cut-off and dimensional regularization. Our new results are in excellent numerical agreement with these, and so we can now conclude with confidence that there is no residual regularization dependence in these results. Moreover, from a computational point of view the regularization independent method has enormous advantages, since all integrals are absolutely convergent by construction, and so do not mix small and arbitrarily large momentum scales. We analytically predict power law behaviour in the asymptotic region, which is confirmed numerically with high precision. The successful demonstration of this efficient new technique opens the way for studies of unquenched QED to be undertaken in the near future.Comment: 20 pages,5 figure

Chiral transition and monopole percolation in lattice scalar QED with quenched fermions

We study the interplay between topological observables and chiral and Higgs transitions in lattice scalar QED with quenched fermions. Emphasis is put on the chiral transition line and magnetic monopole percolation at strong gauge coupling. We confirm that at infinite gauge coupling the chiral transition is described by mean field exponents. We find a rich and complicated behaviour at the endpoint of the Higgs transition line which hampers a satisfactory analysis of the chiral transition. We study in detail an intermediate coupling, where the data are consistent both with a trivial chiral transition clearly separated from monopole percolation and with a chiral transition coincident with monopole percolation, and characterized by the same critical exponent $\nu \simeq 0.65$. We discuss the relevance (or lack thereof) of these quenched results to our understanding of the \chupiv\ model. We comment on the interplay of magnetic monopoles and fermion dynamics in more general contexts.Comment: 29 pages, 13 figures included, LaTeX2e (elsart

The instanton liquid in QCD at zero and finite temperature

In this paper we study the statistical mechanics of the instanton liquid in QCD. After introducing the partition function as well as the gauge field and quark induced interactions between instantons we describe a method to calculate the free energy of the instanton system. We use this method to determine the equilibrium density and the equation of state from numerical simulations of the instanton ensemble in QCD for various numbers of flavors. We find that there is a critical number of flavors above which chiral symmetry is restored in the groundstate. In the physical case of two light and one intermediate mass flavor the system undergoes a chiral phase transition at $T\simeq 140$ MeV. We show that the mechanism for this transition is a rearrangement of the instanton liquid, going from a disordered, random, phase at low temperatures to a strongly correlated, molecular, phase at high temperature. We also study the behavior of mesonic susceptibilities near the phase transition.Comment: 50 pages, revtex, 16 figures, uuencode