Cumulant Expansion

David R. Reichman, Frank L. H. Brown, Peter Neu

The dynamics of the dissipative two-level system at zero temperature is studied using three different cumulant expansion techniques. The relative merits and drawbacks of each technique are discussed. It is found that the noncrossing cumulant expansion technique appears to embody the virtues of the more standard cumulant methods.

Peter Fulde

Yu Xia, Hao Che, D. L. Lin +1 more

It is shown for the Ising model that the linked-cluster expansion (LCE) is a special case of the variational cumulant expansion (VCE) in the high-temperature limit. The VCE was originally developed and formulated to treat lattice-gauge-field models. The free energy calculated from the VCE with a trial Hamiltonian of mean-field form in the high-temperature limit is in fact identical to that from the LCE. Thus, a more general expansion that is valid for the whole temperature range is established for the treatment of Ising systems.

Peter Kopietz, Lorenz Bartosch, Florian Schütz

A. J. Berlinsky, A. Brooks Harris

Ruijie Liu, T. L. Chen

The variational-cumulant-expansion (VCE) method is adopted to calculate the Heisenberg model. The free energy of the model is expanded to the third order, and the analytical formulas for the critical temperature ${\mathit{T}}_{\mathit{c}}$ are given for each order. The first order of VCE corresponds to the mean-field theory, the second order gives the same result for ${\mathit{T}}_{\mathit{c}}$ as the 1/z expansion, and the third order gives a more complicated correction. As a comparison, the results of the two-dimensional (2D) Ising model for VCE to the seventh order are shown. We carry out a trial to predict the critical temperature of the infinite order of the VCE, and get a very accurate result for the 2D Ising model. A prediction of ${\mathit{T}}_{\mathit{c}}$ for the Heisenberg model is also made.