Iterating block spin transformations of the O(3) nonlinear {sigma} model

Journal Article · Mon Jul 01 00:00:00 EDT 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.54.1736· OSTI ID:286249

Gottlob, A P ^[1]; Hasenbusch, M ^[2]; Pinn, K ^[3]

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1. Fachbereich Physik, Universitaet Kaiserslautern, D-67653 Kaiserslautern (Germany)
2. DAMTP, Silver Street, Cambridge, CB3 9EW (England)
3. Institut fuer Theoretische Physik I, Universitaet Muenster, Wilhelm-Klemm-Strasse 9, D-48149 Muenster (Germany)

We study the iteration of block spin transformations in the O(3) symmetric nonlinear {sigma} model on a two-dimensional square lattice with the help of the Monte Carlo method. In contrast with the classical Monte Carlo renormalization group approach, we {ital do} attempt to explicitly compute the block spin effective actions. Using two different methods for the determination of effective couplings, we study the renormalization group flow for various parametrization and truncation schemes. The largest ansatz for the effective action contains thirteen coupling constants. Actions on the renormalized trajectory should describe theories with no lattice artifacts, even at a small correlation length. However, tests with the step scaling function of L{umlt u}scher, Weisz, and Wolff reveal that our truncated effective actions show sizable scaling violations indicating that the {ital Ans{umlt a}tze} are still too small. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 286249
• Journal Information: Physical Review, D, Vol. 54, Issue 2; Other Information: PBD: Jul 1996
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
SIGMA MODEL
TRANSFORMATIONS
SPIN
NONLINEAR PROBLEMS
O GROUPS
MONTE CARLO METHOD
TWO-DIMENSIONAL CALCULATIONS
LATTICE FIELD THEORY
RENORMALIZATION
COUPLING CONSTANTS
SCALING
VIOLATIONS