Hamiltonian studies of thed=2Ashkin-Teller model

Abstract

We study a one-dimensional quantum Hamiltonian problem which is equivalent to a highly anisotropic version of the two-dimensional Ashkin-Teller model. This problem is studied by using its duality and other symmetry properties, by a consideration of its limiting cases, and by mapping it into an $\mathrm{XXZ}$ linear chain which is equivalent to a highly anisotropic six-vertex model. In addition eleventh-order strong-coupling series are used to derive numerical data about the Hamiltonian problem. By these means a phase diagram is obtained. The essentially new feature of this diagram is a "critical fan," i.e., a region where a line of continuously varying criticality "fans out" and becomes an area of critical behavior.