Exactly Solved Models

M A Moore

R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Tohru Morita, Kazuyuki Tanaka

It is shown that there exists a generalized Heisenberg model of half-odd-integral spin S greater than 1/2 corresponding to the model of spin 1/2, and we have exactly solved models of half-odd-integral spin S greater than 1/2 corresponding to exactly solved models of spin 1/2.

Er’el Granot

Abstract The Landau-Zener formula represents the only case where a dynamic quantum system was solved exactly analytically. There is no model of a system, which is perturbed by a temporal pulse, and can be solved exactly. It is suggested to use a delta-function perturbation, a model which has an exact analytical solution, to model the effect of a finite period pulse perturbation. Not only can this model be solved exactly and mimic the effect of a very narrow pulse, but it also presents a quantization rule for suppressed transmission ( i.e. , no change in initial state), which resembles qualitatively a similar quantization rule that appears due to the presence of a finite period pulse. Nevertheless, despite its simplicity, the model exhibits non-trivial dynamics that challenge approximation schemes. Specifically, it shows that the suppressed transmission criterion substantially changes due to an arbitrarily small change in potential value.