Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation   in Excitation Energy -
  We investigate excitation energies of hyperbolically deformed S = 1 spin chains, which are specified by the local energy scale f_j^{~} = \cosh j \lambda, where j is the lattice index and \lambda is the deformation parameter. The elementary excitation is well described by a quasiparticle hopping model, which is also expressed in the form of hyperbolic deformation. It is possible to estimate the excitation gap \Delta in the uniform limit \lambda \rightarrow 0, by means of a finite size scaling with respect to the system size N and the deformation parameter \lambda. 
Hiroshi Ueda, Hiroki Nakano, Koichi Kusakabe, and Tomotoshi Nishino
cond-mat.str-el cond-mat.other