Thermodynamic study of a lattice of compass needles in dipolar interaction

We present the study of an original system, which is an experimental dipolar model allowing a precise understanding of dipolar effects. This system is a square lattice of $22\times 22$ magnetized needles (compass needles). Its thermodynamic properties are studied by considering the action of a random external field supposed to mimic the thermal fluctuations. In parallel, a Monte Carlo numerical simulation of the experimental system is performed. Both studies show the existence of a phase transition between an ordered phase and a disordered one. We introduce the notion of “line length” which is the relevant quantity to describe the obtained configurations and to give a precise description of the observed transition. This phase transition is characterized by the emergence of a preferential direction, called the “director,” and by an increase of the average line length. The order parameter expressing the symmetry breaking is defined. Our results show an example of a successful mapping of a dynamic dissipative system excited by a random field onto equilibrium statistical mechanics.