Continuum Limit and Improved Action in Lattice Theories. 1. Principles and phi**4 Theory

Corrections to continuum theory results stemming from finite lattice spacing can be diminished systematically by use of lattice actions that also include suitable irrelevant terms. We describe in detail the principles of such constructions for the example of the φ4 theory.

[1]  Gerard 't Hooft,et al.  Dimensional regularization and the renormalization group , 1973 .

[2]  F. David.  QUANTIZATION WITH A GLOBAL CONSTRAINT AND IR FINITENESS OF TWO-DIMENSIONAL GOLDSTONE SYSTEMS , 1981 .

[3]  Monte Carlo Study of Noncompact Lattice {QCD} , 1981 .

[4]  F. David.  Cancellations of infrared divergences in the two-dimensional non-linear σ models , 1981 .

[5]  S. Elitzur.  The Applicability of Perturbation Expansion to Two-dimensional Goldstone Systems , 1983 .

[6]  C. Itzykson,et al.  Functional methods and perturbation theory , 1975 .

[7]  W. Zimmermann.  Normal products and the short distance expansion in the perturbation theory of renormalizable interactions , 1973 .

[8]  Non-perturbative effects in two-dimensional lattice O(N) models , 1981 .

[9]  I. Montvay,et al.  Improved continuum limit in the lattice O(3) non-linear sigma model , 1983 .

[10]  Sergio Caracciolo,et al.  Polymers and g|φ|4 theory in four dimensions , 1983 .

[11]  P. Hasenfratz,et al.  The connection between the Λ parameters of lattice and continuum QCD , 1980 .

[12]  B. Dewitt.  QUANTUM THEORY OF GRAVITY. II. THE MANIFESTLY COVARIANT THEORY. , 1967 .

[13]  G. Parisi.  On the relation between the renormalized and the bare coupling constant on the lattice , 1980 .

[14]  J. Lowenstein.  Differential vertex operations in Lagrangian field theory , 1971 .

[15]  K. Symanzik,et al.  Continuum Limit and Improved Action in Lattice Theories. 2. O(N) Nonlinear Sigma Model in Perturbation Theory , 1983 .

[16]  Improving the lattice action near the continuum limit , 1982 .

[17]  K. Symanzik.  Renormalization problem in nonrenormalizable massless Φ4 theory , 1975 .

[18]  S. Coleman.  There are no Goldstone bosons in two dimensions , 1973 .

[19]  D. Amit,et al.  The O(n)-symmetric model between two and four dimensions , 1981 .

[20]  R. Wohlert,et al.  Continuum limit improved lattice action for pure Yang-Mills theory (I)☆ , 1983 .

[21]  N. Mermin,et al.  Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models , 1966 .

[22]  W. Zimmermann.  Composite operators in the perturbation theory of renormalizable interactions , 1973 .

[23]  D. Amit,et al.  Cross-over behavior of the nonlinear σ-model with quadratically broken symmetry , 1978 .

[24]  Current conservation in perturbation theory for the non-linear O(N) sigma model , 1981 .