Field-Theoretic Reference State The Einstein Crystal of Grid-Based Fields

Field-Theoretic Reference State The Einstein Crystal of Grid-Based Fields 

The spring constants, a , should be chosen as to minimize the absolute value of integrand of Eq. (5.66) as a function ofX [112]. Note that in simple crystals in hard condensed matter, all particles fluctuate around the ideal lattice position by the same amount. The fluctuations of the fields, AW (c), in a self-assembled structure, however, depend on the spatial position, c. 

Particle-Based Approach Reversible Path in External Ordering Held 

1 How to Turn a Disordered Meh into a Microphase-Separated Morphology Without Passing Through a First-Order Transition  

Within a particle-based model, there is no well-defined reference state for the self-assembled structure. However, one can try to relate the seF-assembled structure to a disordered melt (or a different self-assembled morphology) via a reversible path and calculate the change of the free energy by thermodynamic integration. Typically, transitions between disordered and ordered morphologies or between different self-assembled structures are of first order. Thus, in an analogy to crystallization of hard condensed matter, there is no path in the space of physical intensive variables - for example, temperature, incompatibility, or composition - that reversibly cormects disordered and ordered structures. 

---