Phase Transitions in a Mechanical System Coupled to Glauber Spins Articles uri icon

publication date

  • June 2010

start page

  • 6016

volume

  • 2010

International Standard Serial Number (ISSN)

  • 1742-5468

abstract

  • A harmonic oscillator linearly coupled with a linear chain of Ising spins is investigated. The N spins in the chain interact with their nearest neighbours with a coupling constant proportional to the oscillator position and to N − 1/2, are in contact with a thermal bath at temperature T,
    and evolve under Glauber dynamics. The oscillator position is a
    stochastic process due to the oscillator&-spin interaction which produces
    drastic changes in the equilibrium behaviour and the dynamics of the
    oscillator. Firstly, there is a second order phase transition at a
    critical temperature Tc whose order parameter is the oscillator stable rest position: this position is zero above Tc and different from zero below Tc.
    This transition appears because the oscillator moves in an effective
    potential equal to the harmonic term plus the free energy of the spin
    system at fixed oscillator position. Secondly, assuming fast spin
    relaxation (compared to the oscillator natural period), the oscillator
    dynamical behaviour is described by an effective equation containing a
    nonlinear friction term that drives the oscillator towards the stable
    equilibrium state of the effective potential. The analytical results are
    compared with numerical simulation throughout the paper.