Statics and dynamics of a harmonic oscillator coupled to a   one-dimensional Ising system
  We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the oscillator stable rest position as its order parameter. Secondly, for fast spins, the oscillator dynamics is described by an effective equation with a nonlinear friction term that drives the oscillator towards the stable equilibrium state. 
A. Prados, L. L.Bonilla and A.Carpio
cond-mat.stat-mech math-ph math.MP