Large Orders for Self-Avoiding Membranes

Details Large Orders for Self-Avoiding Membranes Large Orders for Self-Avoiding Membranes

1998-07-10

arxiv.org/abs/cond-mat/9807160v1

Nucl.Phys.B535:555-595,1998

Physics

Condensed Matter

40 pages Latex, 32 eps-files included in the text

Scientific paper

10.1016/S0550-3213(98)00667-1

We derive the large order behavior of the perturbative expansion for the continuous model of tethered self-avoiding membranes. It is controlled by a classical configuration for an effective potential in bulk space, which is the analog of the Lipatov instanton, solution of a highly non-local equation. The n-th order is shown to have factorial growth as (-cst)^n (n!)^(1-epsilon/D), where D is the `internal' dimension of the membrane and epsilon the engineering dimension of the coupling constant for self-avoidance. The instanton is calculated within a variational approximation, which is shown to become exact in the limit of large dimension d of bulk space. This is the starting point of a systematic 1/d expansion. As a consequence, the epsilon-expansion of self-avoiding membranes has a factorial growth, like the epsilon-expansion of polymers and standard critical phenomena, suggesting Borel summability. Consequences for the applicability of the 2-loop calculations are examined.

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