The toric code gets its name from its periodic boundary conditions, giving it the shape of a torus.
12.
:The same computation for periodic boundary condition ( and still 0 } } ) requires the transfer matrix formalism.
13.
These are often used with periodic boundary conditions on the region simulated and Ewald summation techniques are used to speed up computations.
14.
:: It's easier to solve when you impose periodic boundary conditions, because then the system is invariant under translations.
15.
Summing over the states of the bonds in the first row with the periodic boundary conditions i _ 1 = i'_ 1, gives
16.
These equations determine \ psi in terms of the k's, which, in turn, are determined by the periodic boundary conditions.
17.
For example, this happens in six vertex model : the bulk free energy is different for periodic boundary conditions and for domain wall boundary conditions.
18.
If we impose periodic boundary conditions so that every coin can be the starting point ( for large N this doesn't matter much ).
19.
Particles leaving through one side of a cell are simply inserted at the other side ( periodic boundary conditions ); the same goes for the forces.
20.
However, in principle, any DLCQ basis with periodic boundary conditions may include them as constrained modes, dependent on the other modes with nonzero momentum.
