Critical behavior of the three-dimensional ising model from an extended low temperature expansion of the inverse correlation length

We introduce a new method for the derivation of high-order low-temperature expansions of the inverse correlation length and present an O( u 8 ) expansion for the Ising model on a 3-dimensional simple cubic lattice. This corresponds to an O( ν 16 ) high-temperature expansion for the dual model with 4-spin interaction which is equivalent to the 3-dimensional Z 2 lattice gauge theory. The preliminary series analysis admits the rough estimates u c = 0.4079(58), u 1 = -0.1368(74) and u 2 =-0.296(11) for the location of the physical and two unphysical singularities in the complex u -plane. The critical exponent v ′ at u c , u 1 and u 2 is determined as 2 v ′= 1.255(17),,2 v ′= 0.008(1) and 2 v ′ = 0.80(2) respectively. Finally, we indicate further applications of our method