Mean field theory of directed polymers with random complex weights

Theory of directed polymers.

We develop a theory of polymers in a nematic solvent by exploiting an analogy with two-dimensional quantum bosons at zero temperature. We argue that the theory should also describe polymers in an isotropic solvent. The dense phase is analyzed in a Bogoliubovlike approximation, which assumes a broken symmetry in the phase of the boson order parameter. We find a stiffening of the longitudinal flu...

Mean-field theory for interchain orientational ordering of conjugated polymers.

We consider a generalized anisotropic planar-rotor model on a triangular lattice for interchain orientational ordering of undoped and doped polyacetylene, and investigate the effects of various terms on the symmetry and the range of stability of the observed herringbone (HB) phases. Dipole, quadrupole, and octopole interactions are included in the model with sixfold crystal-field anisotropy and...

Renormalized field theory of collapsing directed randomly branched polymers.

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model para...

Random-field Blume-Capel model: Mean-field theory.

Weighted Mean Field Theory for the Random Field Ising Model

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe critical behavior arising from the weighted sum. The resulting exponents are calculated.