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John B. Kogut

Publications and source records attributed to John B. Kogut.

27 records · Page 2Linked to original sources
arXiv1997

Phase Structure of Dynamical Triangulation Models in Three Dimensions

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling mu to the order of the vertices. Monte Carlo renormalization group and finite size scaling techniques are used to locate and characterize this line. Our results indicate that for mu < mu1 ~ -1.0 the model is always in a crumpled phase independent of the value of the curvature coupling. For mu < 0 the results are in agreement with an approximate mean field treatment. We find evidence that this line corresponds to first order transitions extending to positive mu. However, the behavior appears to change for mu > mu2 ~ 2-4. The simplest scenario that is consistent with the data is the existence of a critical end point.

hep-lat↗
arXiv1997

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 $ν\simeq 0.65$. 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.

hep-lat↗
arXiv1997

Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model

We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean dimensions. Different model equations of state, corresponding to different theoretical scenarios, are tested against the order parameter data. The results are sensitive to necessary assumptions about the shape and extent of the scaling region. Our best fits favour a trivial scenario in which the logarithmic corrections are qualitatively similar to those predicted by the large N_f approximation. This is supported by a separate analysis of finite volume corrections for data taken directly in the chiral limit.

hep-lat↗
arXiv1996

Lattice Gauge Theory Simulations at Nonzero Chemical Potential in the Chiral Limit

We present a method of simulating lattice QCD at nonzero chemical potential in the chiral limit. By adding a weak four-fermi interaction to the standard staggered fermion SU(3) QCD action, we produce an algorithm in which the limit of massless fermions is well-behaved and physical. Using configurations at zero chemical potential, and an exact fugacity expansion of the fermion determinant, we can simulate QCD at nonzero chemical potential and evade the notorious problem of the complex action. Small lattice simulations give physical results: At strong gauge coupling the critical chemical potential μ_c agrees with theoretical expectations and at weak gauge coupling μ_c is nonzero in the low temperature confined phase of QCD and jumps to zero in the high temperature quark-gluon plasma phase. In all these simulations the quarks are exactly massless and there is a Goldstone pion.

hep-lat↗
arXiv1995

Electromagnetic Self-Duality in a Lattice Model

We formulate a Euclidean lattice theory of interacting elementary spin-half electric and magnetic charges, which we refer to as electrons and magnetic monopoles respectively. The model uses the polymer representation of the fermion determinant, and exhibits a self-dual symmetry provided electric charge $e$ and magnetic charge $g$ obey the minimal Dirac quantisation condition $eg=2π$. In a hopping parameter expansion at lowest order, we show that virtual electron and monopole loops contribute radiative corrections of opposite sign to the photon propagator. We argue that in the limit $e\to0$, fermion mass $μ\to0$, the model describes QED together with strongly interacting monopoles whose chiral symmetry is spontaneously broken. Prospects for the existence of an interacting continuum limit at the self-dual point $e=g$ are discussed.

hep-lat↗
arXiv1993

Three-Dimensional Quantum Gravity Coupled to Gauge Fields

We show how to simulate U(1) gauge fields coupled to three-dimensional quantum gravity and then examine the phase diagram of this system. Quenched mean field theory suggests that a transition separates confined and deconfined phases (for the gauge matter) in both the negative curvature phase and the positive curvature phase of the quantum gravity, but numerical simulations find no evidence for such transitions.

hep-lat↗
arXiv1992

Four - Fermi Theories in Fewer Than Four Dimensions

Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes relativistic fermions interacting non-trivially via exchange of scalar bound states. We calculate the $O(1/N_f)$ corrections to this picture, where $N_f$ is the number of fermion species, for a variety of models and confirm their renormalizability to this order. A connection between renormalizability and the hyperscaling relations between the theory's critical exponents is made explicit. We present results of extensive numerical simulations of the simplest model for $d=3$, performed using the hybrid Monte Carlo algorithm on lattice sizes ranging from $8^3$ to $24^3$. For $N_f=12$ species of massless fermions we confirm the existence of a second order phase transition where chiral symmetry is spontaneously broken. Using both direct measurement and finite size scaling arguments we estimate the critical exponents $β$, $γ$, $ν$ and $δ$. We also investigate symmetry restoration at non-zero temperature, and the scalar two-point correlation function in the vicinity of the bulk transition. All our results are in excellent agreement with analytic predictions, and support the contention that the $1/N_f$ expansion is accurate for this class of models.

hep-lat↗
arXiv1992

Numerical Study of c>1 Matter Coupled to Quantum Gravity

We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier' in two dimensional quantum gravity. We study multiple Ising models living on dynamical $ϕ^3$ graphs and analyse the behaviour of moments of the graph loop distribution. We notice a universality at work as the average properties of typical graphs from the ensemble are determined only by the central charge. We further argue that the qualitative nature of these results can be understood from considering the effect of fluctuations about a mean field solution in the Ising sector.

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