Thermodynamics of elementary excitations in artificial magnetic square ice

We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. Emphasis is given to the effects of temperature on elementary excitations (magnetic monopoles and their 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 with opposite charges exhibit a sharp peak and a local maximum, respectively, at the same temperature, T-p approximate to 7.2D/k(B) (here, D is the strength of the dipolar interaction and k(B) the Boltzmann constant). When the lattice size is increased, the amplitude of these features also increases but very slowly. Really, the specific heat and the maximum of the average separation dmax between oppositely charged monopoles increase logarithmically with 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 >= 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.