Nature of perturbation theory in spin glasses

Abstract

The high-order behavior of the perturbation expansion in the cubic replica field theory of spin glasses in the paramagnetic phase has been investigated. The study starts with the zero-dimensional version of the replica field theory and this is shown to be equivalent to the problem of finding finite size corrections in a modified spherical spin glass near the critical temperature. We find that the high-order behavior of the perturbation series is described, to leading order, by coefficients of alternating signs (suggesting that the cubic field theory is well-defined) but that there are also subdominant terms with a complicated dependence of their sign on the order. Our results are then extended to the d-dimensional field theory and in particular used to determine the high-order behavior of the terms in the expansion of the critical exponents in a power series in epsilon=6-d. We have also corrected errors in the existing epsilon expansions at third order.

12 pages, 7 figures

References in corpus (2)

• Summability of the perturbative expansion for a zero-dimensional disordered spin model
• Free energy fluctuations in Ising spin glasses

Cited by in corpus (8)

• Finite size corrections in the Sherrington-Kirkpatrick model
• Nontrivial critical fixed point for replica-symmetry-breaking transitions
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
• Two-Loop Corrections to Large Order Behavior of ${\phi }^4$ Theory
• Composite operators in Cubic Field Theories and Link Overlap Fluctuations in Spin-Glass Models