One-Dimensional Classical Planar Model with Competing Interactions

Abstract

Exact results for the thermodynamic properties of the one-dimensional classical planar model with competing nearest-neighbor and next-nearest-neighbor interactions are presented. The calculations are performed by extending the numerical transfer-matrix method of the nearest-neighbor problem to allow for next-nearest-neighbor interactions. It is found that, for a certain range of values of the competing interactions, the system exhibits helical short-range order whose characteristic wave-number depends on temperature. The nature of the helical short-range order at low temperatures is discussed in connection with a domain wall between domains of opposing chirality of the helical state.