Mean-field theory of the phase diagram of ultrasoft, oppositely charged polyions in solution

2012 ◽  
Vol 137 (9) ◽  
pp. 094905 ◽  
Author(s):  
Arash Nikoubashman ◽  
Jean-Pierre Hansen ◽  
Gerhard Kahl
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Mean Field Theory ◽  
Mean Field ◽  
Oppositely Charged

Pinwheel and herringbone structures of planar rotors with anisotropic interactions on a triangular lattice with vacancies

1984 ◽  
Vol 62 (9) ◽  
pp. 915-934 ◽  
Author(s):  
A. B. Harris ◽  
O. G. Mouritsen ◽  
A. J. Berlinsky
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Mean Field Theory ◽  
Mean Field ◽  
Wave Theory ◽  
Finite Domain ◽  
Unexpected Result ◽  
Spin Wave Theory

A variety of theoretical techniques, including Monte Carlo (MC), mean field theory, and spin-wave theory, are used to analyze the phase diagram of a system of planar rotors on a triangular lattice with vacancies. A simple anisotropic interaction, which mimics the electric quadrupole–quadrupole interaction for diatomic molecules confined to rotate in the plane of the surface, induces a herringbone-ordered structure for the pure (x = 1) system, whereas for x ≈ 0.75, if the vacancies are free to move, a 2 × 2 pinwheel structure is favored. For x = 0.75, MC calculations give a continuous transition with Ising exponents in agreement with renormalization group predictions for this universality class, the Heisenberg model with corner-type cubic anisotropy. Mean field theory gives the unexpected result that the pinwheel phase is stable only along the herringbone-disordered state coexistence line in the temperature versus chemical potential phase diagram. Spin-wave theory is used to show that there is, in fact, a finite domain of stability for the pinwheel phase, and a complete phase diagram, which encompasses all available information, is conjectured.

THE MEAN-FIELD THEORY OF DIRECTED POLYMERS IN RANDOM MEDIA AND SPIN GLASS MODELS

1995 ◽  
Vol 07 (02) ◽  
pp. 183-192 ◽  
Author(s):  
F. KOUKIOU
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Glass ◽  
Spin Glasses ◽  
Random Media ◽  
Random Medium ◽  
Mean Field Theory ◽  
Mean Field ◽  
Directed Polymers ◽  
The Mean

We give a unifying framework for the mean-field theory for models of spin glasses and directed polymers in a random medium defined on homogeneous graphs. Their phase diagram is studied in the complex plane of temperature.

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