Topological susceptibility on the lattice: The two-dimensional O(3). sigma. model

Journal Article · Sun Nov 15 00:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.4630· OSTI ID:7002602

Di Giacomo, A ^[1]; Farchioni, F; Papa, A; Vicari, E ^[2]

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1. Dipartimento di Fisica dell'Universita and Istituto Nazionale di Fisica Nucleare, Piazza Torricelli 2, I-56100 Pisa (Italy) CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)
2. Dipartimento di Fisica dell'Universita and Istituto Nazionale di Fiscia Nucleare, Piazza Torricelli 2, I-56100 Pisa (Italy)

As a test of the procedures used in lattice gauge theories, we study the topological susceptibility {chi} in a two-dimensional O(3) {sigma} or CP{sup 1} model. We determine {chi} by defining the density of topological charge as a local operator on the lattice. Following the prescriptions of field theory we perform the additive and multiplicative renormalizations needed to extract {chi} from Monte Carlo data. We also determine {chi} by the cooling method, finding consistent results. A combined use of cooling and field theory again gives the same result and insight into the renormalization mechanism. Finally we give a direct determination, by Monte Carlo techniques, of both the multiplicative and additive renormalizations, by heating configurations with a definite number of instantons. The results are consistent with perturbation theory.

• OSTI ID: 7002602
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 46:10; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LATTICE FIELD THEORY
SIGMA MODEL
CHARGE DENSITY
CP INVARIANCE
GAUGE INVARIANCE
MONTE CARLO METHOD
O GROUPS
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
RENORMALIZATION
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES
WARD IDENTITY
BOSON-EXCHANGE MODELS
DYNAMICAL GROUPS
FIELD THEORIES
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICS
PARTICLE MODELS
PERIPHERAL MODELS
QUANTUM FIELD THEORY
SYMMETRY GROUPS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
662120 - General Theory of Particles & Fields- Symmetry
Conservation Laws
Currents & Their Properties- (1992-)
662230 - Quantum Chromodynamics- (1992-)