  We derive thermodynamically consistent models for diblock copolymer solutions
coupled with the electric and magnetic field, respectively. These models
satisfy the second law of thermodynamics and therefore are therefore
thermodynamically consistent. We then design a set of 2nd order, linear,
semi-discrete schemes for the models using the energy quadratization method and
the supplementary variable method, respectively, which preserve energy
dissipation rates of the models. The spatial discretization is carried out
subsequently using 2nd order finite difference methods, leading to fully
discrete algorithms that preserve discrete energy-dissipation-rates of the
models so that the resulting fully discrete models are thermodynamically
consistent. Convergence rates are numerically confirmed through mesh refinement
tests and several numerical examples are given to demonstrate the role of the
mobility in pattern formation, defect removing effect of both electric and
magnetic fields as well as the hysteresis effect for applied external fields in
copolymer solutions.
