Quantitative Picture of the Scaling Behavior of Lattice Nonlinear $\sigma$ Models From the 1/$N$ Expansion

Biscari, Paolo; Campostrini, Massimo; Rossi, Paolo

doi:10.1016/0370-2693(90)91462-K

Quantitative Picture of the Scaling Behavior of Lattice Nonlinear $\sigma$ Models From the 1/ $N$ Expansion

Paolo Biscari
(
- Pisa, Scuola Normale Superiore and
- INFN, Pisa
)
,
Massimo Campostrini
(
- Pisa U. and
- INFN, Pisa
)
,
Paolo Rossi
(
- Pisa U. and
- INFN, Pisa
)

Feb, 1990

9 pages

Published in:

Phys.Lett.B 242 (1990) 225-233

Published: 1990

DOI:

10.1016/0370-2693(90)91462-K

Report number:

IFUP-TH-7/90

View in:

ADS Abstract Service

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Abstract: (Elsevier)

We evaluate the 1/ N contributions to the mass gap and to the magnetic susceptibility for the two-dimensionalO (N) nonlinear σ-model with standard lattice action. By a new asymptotic expansion of the effective propagator we obtain explicit representations of the scaling (field-theoretical) parts of these quantities and analytic expressions for their ratios to the Λ parameter. Renormalization group functions can be reconstructed and shown to be consistent with universality. Numerical evaluation of the effective Feynman diagrams is performed in a range including the onset of scaling. By comparing the two approaches we recognize that the breakdown of scaling is due to irrelevant dimension four operators contained in the lattice action. The onset of scaling occurs at β≡1/NT⋍0.8 .

sigma model: nonlinear
dimension: 2
symmetry: O(N)
lattice field theory
expansion 1/N
mass spectrum
scaling
propagator
perturbation theory: higher-order
renormalization group

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