Compositeness, Triviality and Bounds on Critical Exponents for Fermions and Magnets

Abstract

We argue that theories with fundamental fermions which undergo chiral symmetry breaking have several universal features which are qualitatively different than those of theories with fundamental scalars. Several bounds on the critical indices $\delta$ and $\eta$ follow. We observe that in four dimensions the logarithmic scaling violations enter into the Equation of State of scalar theories, such as $\lambda {\varphi }^4$, and fermionic models, such as Nambu-Jona-Lasinio, in qualitatively different ways. These observations lead to useful approaches for analyzing lattice simulations of a wide class of model field theories. Our results imply that $\lambda {\varphi }^4$ {\it cannot} be a good guide to understanding the possible triviality of spinor $QED$.

12 pages, 3 figures (not included), ILL-(TH)-93-21

References in corpus (4)

• Four - Fermi Theories in Fewer Than Four Dimensions
• Monopole Percolation and The Universality Class of the Chiral Transition in Four Flavor Noncompact Lattice QED
• Universal Properties of Chiral Simmetry Breaking
• Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models

Cited by in corpus (22)

• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models
• Gauged Nambu-Jona Lasinio Studies of the Triviality of Quantum Electrodynamics
• Chiral Susceptibilities in noncompact QED: a new determination of the $\gamma$ exponent and the critical couplings
• Nontriviality of Abelian gauged Nambu-Jona-Lasinio models in four dimensions
• Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model
• The gauged Nambu - Jona Lasinio model: a mean field calculation with non mean field exponents
• The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction
• The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction
• Strongly Coupled QED
• Testing logarithmic violations to scaling in strongly coupled QED
• Renormalization Group Analysis of a Gursey Model Inspired Field Theory
• Gauged System Mimicking the Gürsey Model
• Another Model with Interacting Composites
• A Model with Interacting Composites
• The Landau Pole at Finite Temperature
• Chiral condensate, susceptibilities, critical coupling and indices in QED${}_4$
• More on strongly coupled quenched QED
• Probing the Continuum Limit in Non-Compact QED: New Results on Large Lattices
• Renormalization Group Analysis of a Gursey Model Inspired Field Theory II
• The Continuum Limit of Non Compact QED
• Log Triviality in the Nambu -- Jona-Lasinio Model