We present the numerical study of chaos in a classical model of /N coupled rotators on a lattice, in dimensions /d=2,3. The coupling constants decay with distance as rij-α (/α>=0). The thermodynamics of the model is extensive if /α/d>1 and nonextensive otherwise. For energies above a critical threshold Uc the largest Lyapunov exponent scales as N-κ, where /κ is a universal function of /α/d. The function /κ decreases from /1/3 to /0 when /α/d increases from /0 to /1, and vanishes above 1. We conjecture that this scaling law is related to the nonextensivity of the model, through a power-law sensitivity to initial conditions (weak mixing).
Classical Spin Systems with Long-range Interactions: universal reduction of mixing / A., Campa; Giansanti, Andrea; D., Moroni; C., Tsallis. - In: PHYSICS LETTERS. - ISSN 0031-9163. - A 286:(2001), pp. 251-256. [10.1016/S0375-9601(01)00440-6]
Classical Spin Systems with Long-range Interactions: universal reduction of mixing
GIANSANTI, Andrea;
2001
Abstract
We present the numerical study of chaos in a classical model of /N coupled rotators on a lattice, in dimensions /d=2,3. The coupling constants decay with distance as rij-α (/α>=0). The thermodynamics of the model is extensive if /α/d>1 and nonextensive otherwise. For energies above a critical threshold Uc the largest Lyapunov exponent scales as N-κ, where /κ is a universal function of /α/d. The function /κ decreases from /1/3 to /0 when /α/d increases from /0 to /1, and vanishes above 1. We conjecture that this scaling law is related to the nonextensivity of the model, through a power-law sensitivity to initial conditions (weak mixing).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
