Large N limit of O(N) vector models

We calculate various CFT data for the $O(N)$ vector model with the long-range interaction, working at the next-to-leading order in the $1/N$ expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point $s_\star$ of the exponent parameter $s$. We also develop the $N>1$ generalization of the recently proposed IR duality between ...

We consider classical $O(N)$ vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We prove that such expansions define asymptotic series, and derive explicit estimates on the error terms associated with their finite order truncations. The result applies, in particular, to the spontaneous magnetization of the 3D Heisenberg model. The proof combines a priori bounds on the moments of the ...

For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory is increased. This problem is exacerbated by the fact that perturbation series derived from loop diagram (Feynman diagram) calculations represent asymptotic (divergent) series which limits the predictive power of perturbative quantum field t...

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (also known as the O(N) symmetric Heisenberg classical spin model or the as the lattice O(N) nonlinear sigma model) on the square lattice are extended from order beta^{14} to beta^{21} for arbitrary N. For the second field derivative of the susceptibility the series expansion is extended from order beta^{14} to beta^{17}. For -2 < N < 2, a numerical analysis of...

We propose formulas for the $1/N$ correction to the sphere free energy of theories with 4-fermion interactions, which are conformal for $d>2$. We also propose a formula for the scalar $O(N)$ model. Expanding these formulas in small $\epsilon$ near various integer dimensions we find a perfect agreement with results obtained using $\epsilon$-expansion technique. In $d=3$, the large $N$ results with the $1/N$ correction included are in good agreement with the Pade resummed $\eps...

We study a $T\bar{T}$-deformed $O(N)$ vector model, which is classically equivalent to the Nambu-Goto action with static gauge. The thermal free energy density can be computed exactly by using the Burgers equation as a special property of $T\bar{T}$-deformation. The resulting expression is valid for an arbitrary value of $N$. One may consider a large $N$ limit while preserving this expression. We try to derive this result in the field-theoretical approach directly by employin...

We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar $U(\phib^2)$ field theory for $N$ large and discuss various non-perturbative physical issue...

For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered cubic lattices. (The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on the two latt...

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 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 finite-size-scaling and the perturbative limit do not commute in the calculation of the corrections to finite-size scaling. We present also a deta...

We study the off-equilibrium two-point critical response and correlation functions for the relaxational dynamics with a coupling to a conserved density (Model C) of the O(N) vector model. They are determined in an \epsilon=4-d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in epsilon. The corresponding fluctuation-dissipation ratio has a non trivial large time limit in the aging re...