Rotators with Long-Range Interactions: Connection with the Mean-Field Approximation

F. TAMARIT; C. ANTENEODO

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Año: 2000 vol. 84 p. 208 - 211

0031-9007

We analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as r-α where r is the interparticle distance and α≥0. By integrating the equations of motion we obtain the microcanonical time averages of both the magnetization and the kinetic energy. We detect three different regimes depending on whether α belongs to the intervals [0,1), (1,2), or (2,∞). For 0<α<1, the microcanonical averages agree, after a scaling, with those obtained in the canonical ensemble for the mean-field case (α  =  0). This correspondence offers a mathematically tractable way of dealing with systems governed by slowly decaying long-range interactions.