Perfect lattice action for asymptotically free theories

Abstract There exist lattice actions which give cut-off independent physical predictions even on coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in addition, the classical equations have scale invariant instanton solutions. This perfect action can be made short ranged. It can be determined by combining analytical calculations with numerical simulations on small lattices. We illustrate the method and the benefits on the d = 2 non-linear σ-model.

[1]  I. M. Singer,et al.  Recent Developments in Gauge Theories , 1980 .

[2]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[3]  Advances in lattice gauge theory , 1985 .

[4]  K. Wilson.  The renormalization group: Critical phenomena and the Kondo problem , 1975 .

[5]  Block averaging renormalization group for lattice and continuum euclidean fermions: Expected and unexpected results , 1989 .

[6]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[7]  Alan M. Ferrenberg,et al.  New Monte Carlo technique for studying phase transitions. , 1988, Physical review letters.

[8]  L. Kadanoff.  The application of renormalization group techniques to quarks and strings , 1977 .

[9]  Block renormalization group for Euclidean Fermions , 1989 .

[10]  K. Wilson.  The renormalization group and critical phenomena , 1983 .

[11]  B. M. Fulk.  MATH , 1992 .

[12]  K. Gawȩdzki,et al.  A rigorous block spin approach to massless lattice theories , 1980 .

[13]  On-shell improved lattice gauge theories , 1985 .

[14]  Michael Creutz,et al.  Quantum Fields On The Computer , 1992 .

[15]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

[16]  R. Swendsen.  Monte Carlo Calculation of Renormalized Coupling Parameters , 1984 .

[17]  F. Niedermayer,et al.  General cluster updating method for Monte Carlo simulations. , 1988, Physical review letters.

[18]  Convergent Perturbation Expansions for Euclidean Quantum Field Theory , 1985 .

[19]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[20]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[21]  Xiangxue Li,et al.  Lattice Gauge Theory Using Parallel Processors , 1987 .