Antiperiodic boundary condition

As seen in Fig. 7, crossovers[93] for periodic and antiperiodic boundary conditions separate the neutral and ionic regimes. The dashed line is the extrapolated behavior of the infinite chain. The narrow ionic region at small U becomes a point at U = 0 for the noninteracting system that can readily be solved exactly. Finite... 

Figure 7 Ground-state crossover, U(AC,N), of the modified Hubbard model (36), with periodic and antiperiodic boundary conditions for N = An and An + 2, respectively. The dashed lines are extrapolations to the infinite chain and rigorously passes through the origin. The inset shows the behavior at large site-energy A the limit A —> oo corresponds to the restricted basis in which D+2 and A-2 sites are excluded[97].

Computer simulations can find the interfacial energy by simulating the same lattice first with antiperiodic boundary conditions as described above, and then with periodic boundary conditions and with initially all spins up. Then an interface exists only in the first and not in the second case, and the difference between the first and the... 

In models of Ising ferromagnets a common method to stabilize one interface between spin-up and spin-down phases is the use of antiperiodic boundary conditions in one direction of the system, unit vector in the z-direction (perpendicular to the interface that is stabilized), and L is the linear dimension of the system perpendicular to the interface. In the x,y-directions parallel to the interface, where one then uses linear dimensions which may be chosen different from Li, standard periodic boundary conditions are used ([Pg.391]

Fig. 65. (a) Boundary conditions used to impose at tilled interface in an Ising ferromagnet antiperiodic (APBC) in the z-direction, periodic in the y-direction (PBC), and screw periodic boundary conditions (SPBC) in the x-direction. 

A change of boundary conditions shifts levels corresponding to localized states by an amount of order exp( — rather than This is a very useful condition in numerical studies. In practice, the boundary conditions are changed from periodic to antiperiodic. 

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