A d-dimensional elastic manifold at depinning is described by a
renormalized field theory, based on the Functional Renormalization Group (FRG).
Here we analyze this theory to 3-loop order, equivalent to third order in
ϵ=4−d, where d is the internal dimension. The critical exponent
reads ζ=3ϵ+0.04777ϵ2−0.068354ϵ3+O(ϵ4). Using that ζ(d=0)=2−, we estimate
ζ(d=1)=1.266(20), ζ(d=2)=0.752(1) and ζ(d=3)=0.357(1). For
Gaussian disorder, the pinning force per site is estimated as fc=Bm2ρm+fc0, where m2 is the strength of the confining
potential, B a universal amplitude, ρm the correlation length of
the disorder, and fc0 a non-universal lattice dependent term. For
charge-density waves, we find a mapping to the standard ϕ4-theory with
O(n) symmetry in the limit of n→−2. This gives fc=A~(d)m2ln(m)+fc0, with A~(d)=−∂n[ν(d,n)−1+η(d,n)]n=−2, reminiscent of log-CFTs.Comment: 24 pages, 17 figure