  We investigate the thermodynamics of artificial square spin ice systems
assuming only dipolar interactions among the islands that compose the array.
The emphasis is given on the effects of the temperature on the elementary
excitations (magnetic monopoles and their Dirac strings). By using Monte Carlo
techniques we calculate the specific heat, the density of poles and their
average separation as functions of temperature. The specific heat and average
separation between monopoles and antimonopoles exhibit a sharp peak and a local
maximum, respectively, at the same temperature, $T_{p}\approx 7.2D/k_{B}$
(here, $D$ is the strength of the dipolar interaction and $k_{B}$ is the
Boltzmann constant). As the lattice size is increased, the amplitude of these
features also increases but very slowly. Really, the specific heat and the
maximum in the average separation $d_{max}$ between oppositely charged
monopoles increase logarithmically with the system size, indicating that
completely isolated charges could be found only at the thermodynamic limit. In
general, the results obtained here suggest that, for temperatures $T \geq
T_{p}$, these systems may exhibit a phase with separated monopoles, although
the quantity $d_{max}$ should not be larger than a few lattice spacings for
viable artificial materials.
