v 1 1 A pr 1 99 8 Corrections to Finite - Size Scaling in the Lattice N - Vector Model for N = ∞
نویسنده
چکیده
We compute the corrections to finite-size scaling for the N -vector model on the square lattice in the large-N limit. We find that corrections behave as logL/L2. For tree-level improved hamiltonians corrections behave as 1/L2. In general l-loop improvement is expected to reduce this behaviour to 1/(L2 log L). We show that the finite-size-scaling and the perturbative limit do not commute in the calculation of the corrections to finite-size scaling. We present a detailed study of the corrections for the RP∞-model.
منابع مشابه
Corrections to Finite - Size Scaling in the
We compute the corrections to nite-size scaling for the N-vector model on the square lattice in the large-N limit. We nd that corrections behave as log L=L 2. For tree-level improved hamiltonians corrections behave as 1=L 2. In general l-loop improvement is expected to reduce this behaviour to 1=(L 2 log l L). We show that the nite-size-scaling and the perturbative limit do not commute in the c...
متن کاملar X iv : c on d - m at / 9 81 22 70 v 1 1 6 D ec 1 99 8 First and second order transitions in dilute O ( n ) models
We explore the phase diagram of an O(n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O(n) model, so that n is not restricted to positive integers. For low activities of the vacancies, we observe critical points of the known universality class. At high activities the transition becomes first or...
متن کاملar X iv : h ep - l at / 9 21 00 10 v 1 8 O ct 1 99
Two-dimensional CP models are investigated byMonte Carlo methods on the lattice, for values of N ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length ξ. Several lattice formulations are compared and shown to enjoy scaling for ξ as small as 2.5. Asymptotic scaling is investigated using as bare coupling constant both the usual ...
متن کامل15 v 2 7 O ct 1 99 5 Four - Loop Perturbative Expansion for the Lattice N - Vector Model Sergio
We compute the four-loop contributions to the β-function and the anomalous dimension of the field for the O(N)-invariant N -vector model. These results are used to compute the second analytic corrections to the correlation length and the general spin-n susceptibility.
متن کامل5 M ar 1 99 9 Cutoff and lattice effects in the φ 4 theory of confined systems
We study cutoff and lattice effects in the O(n) symmetric ϕ 4 theory for a d-dimensional cubic geometry of size L with periodic boundary conditions. In the large-n limit above T c , we show that ϕ 4 field theory at finite cutoff Λ predicts the nonuniversal deviation ∼ (ΛL) −2 from asymptotic bulk critical behavior that violates finite-size scaling and disagrees with the deviation ∼ e −cL that w...
متن کامل