Energy states in the linear chain Ising model

Antonio S. T. Pires, N. P. Silva, B. J. O. Franco

Markus Siegert, Dietrich Stauffer

Toshiyuki Hamasaki, Hidetoshi Nishimori

We derive the exact ground-state energies of the random-field Ising chain and ladder. The random fields consist of three possible values for the chain model and bimodal fields for the ladder model. The results are piecewise linear as a function of the random-field strength. The zero-temperature transfer matrix method is used to obtain these results.

Huey Wen Huang

J. R. Faleiro Ferreira

Abstract A recently proposed variational approach is applied to the Ising model. Former results may be improved when a sum of linear chain Hamiltonians is used as an auxiliary Hamiltonian instead of a sum of single particle Hamiltonians.

J. Rosenfeld, N.E. Ligterink

The phase transition present in the linear-chain and square-lattice cases of the transverse Ising model is examined. The extended coupled-cluster method (ECCM) can describe both sides of the phase transition with a unified approach. The correlation length and the excitation energy are determined. The ECCM is able to use both the weak- and the strong-coupling starting states within a calculation based on the same uncorrelated model state.