A phase-field model of relaxor ferroelectrics based on random field theory

A mechanically coupled phase-field model is proposed for the first time to simulate the peculiar behavior of relaxor ferroelectrics. Based on the random field theory for relaxors, local random fields are introduced to characterize the effect of chemical disorder. This generic model is developed from a thermodynamic framework and the microforce theory and is implemented by a nonlinear finite element method. Simulation results show that the model can reproduce relaxor features, such as domain miniaturization, small remnant polarization and large piezoelectric response. In particular, the influence of random field strength on these features are revealed. Simulation results on domain structure and hysteresis behavior are discussed and compared with related experimental results.Comment: 8 figure

The energy spectrum symmetry of Heisenberg model in Fock space

We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry of energy spectrum between its subspace $n$ and the subspace $L-n$ of the Fock space. Our proof is completed by introducing two general quantum operations. One is a flip operation of spin direction and another is a mirror reflection of spin sites.Comment: Revising version, 7 preprint pages, no figures; Published version contains some revisions in Languag