The Phase Diagrams of the Schwinger and Gross-Neveu Models with Wilson Fermions

A new method to analytically determine the partition function zeroes of weakly coupled theories on finite-size lattices is developed. Applied to the lattice Schwinger model, this reveals the possible absence of a phase transition at fixed weak coupling. We show how finite-size scaling techniques on small or moderate lattice sizes may mimic the presence of a spurious phase transition. Application of our method to the Gross-Neveu model yields a phase diagram consistent with that coming from a saddle point analysis.Comment: Talk at LATTICE99, 3 pages, 2 figure

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

Surface modes and parity violation in Schwinger model on the lattice

The phase diagram of the Schwinger model on the lattice with Wilson fermions is investigated in the Hartree-Fock approximation. In case of single flavour (not directly amenable to simulations), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. Hartree-Fock vacuum sustains a nonzero electric field in this broken phase. The phase structure of the model with two flavours is also discussed.Comment: 4 pages, uuencoded compressed PostScript (using uufiles), contribution to LATTICE 9

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 $\beta = 0$ we observe and discuss a possible discrepancy with results obtained by a different method.Comment: 3 pages (2 figures), POSTSCRIPT-file (174 KB), Contribution to Lattice 93, preprint UNIGRAZ-UTP 19-11-9

On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions

There are problems in physics and particularly in field theory which are defined by complex valued weight functions $e^{-S}$ where $S$ is a polynomial action $S: R^n \rightarrow C$. The conditions under which a convergent complex Langevin calculation correctly simulates such integrals are discussed. All conditions on the process which are used to prove proper convergence are defined in the stationary limit.Comment: 8 pages, LaTeX file, preprint UNIGRAZ-UTP 29-09-9

Fluctuation Induced First Order Phase Transitions

We study a $U(N)\times U(N)$ symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum fluctuations. Next, based on the renormalization group and our new simulation results in three dimensions we argue that even if the $U_A(1)$ symmetry is restored below the critical temperature the QCD finite temperature chiral phase transition for two flavor could be extremely weak first order. Contribution to Lattice '93 proceedings. Needs espcrc2.sty file (included). Search Figure1.ps, Figure2.ps, ... for postscript files.Comment: 3 pages, 4 postscript figures attached. Preprint BUHEP-93-2

The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model

In this paper a method previously employed by Salmhofer to establish an exact equivalence of the one-flavour strong coupling lattice Schwinger model with Wilson fermions to some 8-vertex model is applied to the case with two flavours. As this method is fairly general and can be applied to strong coupling QED and purely fermionic models with any (sufficiently small) number of Wilson fermions in any dimension the purpose of the present study is mainly a methodical one in order to gain some further experience with it. In the paper the vertex model equivalent to the two-flavour strong coupling lattice Schwinger model with Wilson fermions is found. It turns out to be some modified 3-state 20-vertex model on the square lattice, which can also be understood as a regular 6-state vertex model. In analogy with the one- flavour case, this model can be viewed as some loop model.Comment: 22 pages LaTe

Complex Langevin Equations and Schwinger-Dyson Equations

Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice are given. Relevance to the study of quantum field theory phase space is discussed.Comment: 23 pages, 4 figures, elsart, typos fixed, includes additional conten