“Color-Tripole Ice” as a Conceptual Generalization of “Spin Ice”
Figure 4
The second two-dimensional model of color-tripole ice. (a) One of the 36 color-tripole crystal states that obey the generalized ice rule for color-tripole ice and preserve the translational symmetries of the lattice. It is made of configurations (a) and (a′) of Figure 1. (b) An example of a “ground state” containing two “collapsed loops,” each of which is made of two finite-and-equal-length color-swap lines that end on the same hexagon on its one end (shaded grey) and on another hexagon on its other end (which is outside the plotted region). (c) A “usual kind” of type-I Y-intersection (at the hexagon marked grey) of three color-swap lines making 120° with each other (enclosed in dotted rectangles). Note that in this case the three color-swap lines all reside on one type of lattice sites (here type A). (d) An “unusual kind” of type-I Y-intersection of three color-swap lines which do not make 120° with each other. We see that both types of lattice sites are now involved in the three color-swap lines in this case.
