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.Comment: 37 pages LaTeX (RevTeX) including 12 .eps figure

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 $\beta$, $\gamma$, $\nu$ and $\delta$. 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.Comment: CERN-TH.6557/92 ILL-(TH)-92-\# 19, 60 pages, 18 figures (not included

Non-Perturbative Renormalization Group Flows in Two-Dimensional Quantum Gravity

Recently a block spin renormalization group approach was proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. We use this approach to examine non-perturbatively a particular class of higher derivative actions for pure gravity.Comment: 17 page

The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $\mu$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $\mu$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.Comment: 42 pages revtex, 25 figures postscrip

On the Triviality of Textbook Quantum Electrodynamics

By adding a small, irrelevant four fermi interaction to the action of lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. This allows an ab initio high precision, controlled study of the existence of "textbook" Quantum Electrodynamics with several species of fermions. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial. The logarithms of triviality, which modify mean field scaling laws, are pinpointed in several observables. The result supports Landau's contention that perturbative QED suffers from complete screening and would have a vanishing fine structure constant in the absence of a cutoff.Comment: reference to Phys. Rev. Lett.80, 4119(1998) adde

Diquark Condensation at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is studied at nonzero chemical potential $\mu$ and temperature $T$ by computer simulation and Effective Lagrangian techniques. Simulations are done on $8^4$, $8^3 \times 4$ and $12^3 \times 6$ lattices and the diquark condensate, chiral order parameter, Wilson line, fermion energy and number densities are measured. Simulations at a fixed, nonzero quark mass provide evidence for a tricritical point in the $\mu$-$T$ plane associated with diquark condensation. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Using Effective Lagrangians we estimate the position of the tricritical point and ascribe its existence to trilinear couplings that increase with $\mu$ and $T$.Comment: 18 pages revtex, 11 figures postscrip