Phase Behavior of Models with Competing Interactions
- 15 March 1971
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 42 (4), 1280-1282
- https://doi.org/10.1063/1.1660214
Abstract
Models with competing nearest‐neighbor and very long‐range interactions are solved exactly for several one‐dimensional cases, including the usual Ising chain (ICCI), the XY model (XYCI), the transverse Ising model (TICCI), and the spherical model (SCCI). For certain ratios of the competing interaction strengths, ICCI and XYCI display triple points and two critical points in a field. In addition TICCI has an apparently enclosed phase in an H‐T phase diagram; however, this phase is really paramagnetic as can be seen when an extended phase diagram is used. The extended phase diagrams for ICCI, XYCI, and TICCI display tricritical points and the tricritical exponents have different values from the usual classical values. In contrast to the rich phase behavior of the preceding models, SCCI shows very simple phase behavior, which is directly related to the ground state. Finally, the introduction of a staggered field to ICCI and a simple transformation allows reinterpretation as a metamagnetic model. Using ICCI as a guide the observability of the tricritical exponents is discussed.Keywords
This publication has 3 references indexed in Scilit:
- Ising Chain with Competing InteractionsPhysical Review A, 1970
- Exact Results in the Kondo Problem. II. Scaling Theory, Qualitatively Correct Solution, and Some New Results on One-Dimensional Classical Statistical ModelsPhysical Review B, 1970
- Thermodynamics Near the Two-Fluid Critical Mixing Point in-Physical Review Letters, 1970