  In this work, we explore a kind of geometrical effect in the thermodynamics
of artificial spin ices (ASI). In general, such artificial materials are
athermal. Here, We demonstrate that geometrically driven dynamics in ASI can
open up the panorama of exploring distinct ground states and thermally magnetic
monopole excitations. It is shown that a particular ASI lattice will provide a
richer thermodynamics with nanomagnet spins experiencing less restriction to
flip precisely in a kind of rhombic lattice. This can be observed by analysis
of only three types of rectangular artificial spin ices (RASI). Denoting the
horizontal and vertical lattice spacings by a and b, respectively, then, a RASI
material can be described by its aspect ratio $\gamma$=a/b. The rhombic lattice
emerges when $\gamma$=$\sqrt{3}$. So, by comparing the impact of thermal
effects on the spin flips in these three appropriate different RASI arrays, it
is possible to find a system very close to the ice regime.
