# Phase transitions in a mechanical system coupled to Glauber spins - Condensed Matter > Statistical Mechanics

Phase transitions in a mechanical system coupled to Glauber spins - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: A harmonic oscillator linearly coupled with a linear chain of Ising spins isinvestigated. The $N$ spins in the chain interact with their nearest neighbourswith a coupling constant proportional to the oscillator position and to$N^{-1-2}$, are in contact with a thermal bath at temperature $T$, and evolveunder Glauber dynamics. The oscillator position is a stochastic process due tothe oscillator-spin interaction which produces drastic changes in theequilibrium behaviour and the dynamics of the oscillator. Firstly, there is asecond order phase transition at a critical temperature $T c$ whose orderparameter is the oscillator stable rest position: this position is zero above$T c$ and different from zero below $T c$. This transition appears because theoscillator moves in an effective potential equal to the harmonic term plus thefree energy of the spin system at fixed oscillator position. Secondly, assumingfast spin relaxation compared to the oscillator natural period, theoscillator dynamical behaviour is described by an effective equation containinga nonlinear friction term that drives the oscillator towards the stableequilibrium state of the effective potential. The analytical results arecompared with numerical simulation throughout the paper.

Author: ** A. Prados, L. L. Bonilla, A. Carpio**

Source: https://arxiv.org/