We evaluate the 1/N contributions to the mass gap and to the magnetic susceptibility for the two-dimensional O(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.
Quantitative picture of the scaling behaviour of lattice nonlinear σ-models from the 1/N expansion
BISCARI, PAOLO;
1990-01-01
Abstract
We evaluate the 1/N contributions to the mass gap and to the magnetic susceptibility for the two-dimensional O(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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
