J.C. Le Guillou

Perturbation theory at large order. I. Theφ2Ninteraction

A new method for calculating the large orders of perturbation theory in quantum field theories has been discussed recently by Lipatov. We show that the same method applied to anharmonic oscillators in quantum mechanics allows one to rederive and generalize results previously obtained by Bender and Wu. We have also verified and generalized Lipatovs results to the case of an internal O(n) symmetry. These results show the divergence of the Wilson-Fisher epsilon expansion and indicate its Borel summability which is used for critical exponents. Similarly, the Callan-Symanzik functions for the phi/sup 4/ theory in three dimensions are characterized.

The hydrogen atom in strong magnetic fields: Summation of the weak field series expansion

Abstract Using the weak field expansion, we have calculated the ground-state energy of the hydrogen atom in a magnetic field for values of the field up to about 10 13 G. The perturbative expansion has been summed by an order-dependent mapping method. We compare our results with previous calculations. Our method allows us to obtain: first, more accurate values of the binding energy for a field up to 10 10 G, then good results in the transition region between the two sets of accurate calculations of the literature, and finally still reasonably accurate values up to 10 13 G.

The H2+ ion in an intense magnetic field: Improved adiabatic approximations

Abstract We study the ground state binding energy of the H 2 + ion in an intense magnetic field. Our calculations are based on improved forms of the adiabatic approximation. We calculate the binding energy, the equilibrium internuclear separation and the zero point energies of nuclear vibrations both parallel and perpendicular to the magnetic field. Comparison of our results with those obtained from the static adiabatic approximation and from variational calculations shows a substantial improvement.

Critical properties near σ dimensions for long-range interactions

The authors show that the critical temperature for n-vector models with long-range interaction falling off at infinity as 1/rd+ sigma vanishes when d= sigma , provided n is larger than one. As a consequence, the authors calculate the critical exponents as power series in (d- sigma ) up to second order.

Perturbation theory at large order. I. The Φ2N interaction

A new method for calculating the large orders of perturbation theory in quantum field theories has been discussed recently by Lipatov. We show that the same method applied to anharmonic oscillators in quantum mechanics allows one to rederive and generalize results previously obtained by Bender and Wu. We have also verified and generalized Lipatovs results to the case of an internal O( n ) symmetry. These results show the divergence of the Wilson-Fisher e expansion and indicate its Borel summability which is used for critical exponents. Similarly, the Callan-Symanzik functions for the Φ 4 theory in three dimensions are characterized.

Theoretical Estimate of the Antiferromagnetic Correlation Length in Doped La2CuO4

We study doped La2CuO4 modelled by a single-band, strongly coupled Hubbard model. Following a proposal of Inui, Doniach and Gabay, we make use of an effective spin Hamiltonian which includes next-nearest-neighbour frustrating couplings. We describe its long-wavelength properties by an O(3) quantum nonlinear sigma-model. We find that antiferromagnetic order survives doping till a critical value δc ≈ 0.067. In this regime we obtain essentially a parameter-free prediction of the correlation length ξ(T) as a function of the doping fraction. It is very substantially reduced with respect to the undoped case, and in very good agreement with the experimental data.

Perturbation Theory at Large Order. 1. The phi**2N Interaction

A new method for calculating the large orders of perturbation theory in quantum field theories has been discussed recently by Lipatov. We show that the same method applied to anharmonic oscillators in quantum mechanics allows one to rederive and generalize results previously obtained by Bender and Wu. We have also verified and generalized Lipatovs results to the case of an internal O(n) symmetry. These results show the divergence of the Wilson-Fisher epsilon expansion and indicate its Borel summability which is used for critical exponents. Similarly, the Callan-Symanzik functions for the phi/sup 4/ theory in three dimensions are characterized.

ABOUT THE CORRELATION LENGTHS OF QUANTUM HEISENBERG FERRO AND ANTIFERROMAGNETS

The mass gap for the two-dimensional O(3) non-linear sigma model has been recently extracted from the Bethe Ansatz solution. Combining this result with the Renormalization Group treatment of the Quantum Heisenberg Ferromagnet as well as the Quantum non-linear sigma model we present new formulas for the correlation length of the square lattice quantum ferro and antiferromagnet.

Perturbation theory at large order. II. Role of the vacuum instability

We extend our previous study of large orders of perturbation series for nonrelativistic quantum mechanics and boson field theories to more complicated situations. It is shown that when perturbation theory is performed around an unstable vacuum and does not reveal any pathology at low orders the existence of real pseudoparticles, which are responsible for the tunneling to a more stable vacuum, also implies the divergence and the non-Borel-summability of the series. Conversely, large orders of perturbations around a stable vacuum are dominated by complex solutions to Euclidean field equations. They quantitatively characterize its behavior and indicate the Borel summability of the series. Thus the corresponding Greens functions are unambiguously determined by their perturbation series.

Perturbation theory at large order. I. The phi/sup 2//sup N/ interaction

A new method for calculating the large orders of perturbation theory in quantum field theories has been discussed recently by Lipatov. We show that the same method applied to anharmonic oscillators in quantum mechanics allows one to rederive and generalize results previously obtained by Bender and Wu. We have also verified and generalized Lipatovs results to the case of an internal O(n) symmetry. These results show the divergence of the Wilson-Fisher epsilon expansion and indicate its Borel summability which is used for critical exponents. Similarly, the Callan-Symanzik functions for the phi/sup 4/ theory in three dimensions are characterized.