Critical behaviour of the 3d Ising model from an extended low-temperature expansion of the inverse correlation length

Abstract

Abstract We introduce a new method for the derivation of high-order low-temperature expansions of the inverse correlation length and present an O(u8) expansion for the Ising model on a 3-dimensional simple cubic lattice. This corresponds to an O(ν16) high-temperature expansion for the dual model with 4-spin interaction which is equivalent to the 3-dimensional Z2 lattice gauge theory. The preliminary series analysis admits the rough estimates uc = 0.4079(58), u1= -0.1368(74) and u2 =-0.296(11) for the location of the physical and two unphysical singularities in the complex u-plane. The critical exponent v ′ at uc, u1 and u2 is determined as 2v′= 1.255(17),,2v′= 0.008(1) and 2v′ = 0.80(2) respectively. Finally, we indicate further applications of our method.