Structural phase transitions in systems of weakly-coupled nonlinear chains

Abstract

Abstract A model Hamiltonian is studied that is characteristic of displacive and order-disorder phase transitions and relevant to certain quasi-one-dimensional ferroelectrics and conductors. Specifically, weakly-coupled two and three dimensional arrays of chains with harmonically coupled local double-well potentials are treated. These systems are mapped1 (in the weak-coupling limit) onto an appropriate Ising model and undergo phase transitions at temperatures Tc. From this mapping it is shown that sub-critical regimes exist both above and below Tc in which the behaviour is essentially that of the one-dimensional Hamiltonian. In particular, signatures of single-chain domain (kink) patterns are apparent. These results and associated dynamic properties are supported with new molecular dynamics simulations.2 The model will be a useful means of understanding the important question3 of the role of intrinsic ‘clusters’ in ‘central peaks’ observed at many structural phase transitions.