Publication: Phase transitions in a mechanical system coupled to Glauber spins
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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 T(c) whose order parameter is the oscillator stable rest position: this position is zero above T(c) and different from zero below T(c). 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.
 Boisen A, 2009 Nat. Nanotechnol. 4 404  Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A and Zwerger W, 1987 Rev. Mod. Phys. 59 1  Bonilla L L and Guinea F, 1992 Phys. Rev. A 45 7718  Feder J and Pytte E, 1973 Phys. Rev. B 8 3978  Rikvold P A, 1978 Z. Phys. B 30 339  Hicke C and Dykman M I, 2008 Phys. Rev. B 78 024401  Glauber R J, 1963 J. Math. Phys. 4 294  Peyrard M, 2006 Nat. Phys. 2 13  Dauxois T, Peyrard M and Bishop A R, 1993 Phys. Rev. E 47 684  Wartell R M and Benight A S, 1985 Phys. Rep. 126 67  Reiss H, 1980 Chem. Phys. 47 15  Brey J J and Prados A, 1993 Physica A 197 569  Brey J J and Prados A, 1996 Phys. Rev. E 53 458  Van Kampen N G, 1997 Stochastic Processes in Physics and Chemistry (Amsterdam: North-Holland)  Reichl L E, 1998 A Modern Course in Statistical Physics (New York: Wiley)  Bragg W L and Williams E J, 1934 Proc. R. Soc. A 145 699  Kafri Y, Mukamel D and Peliti L, 2000 Phys. Rev. Lett. 85 4988  Hanke A, Ochoa M G and Metzler R, 2008 Phys. Rev. Lett. 100 018106  Giaconi G and Toninelli F L, 2006 Phys. Rev. Lett. 96 070602  Brey J J and Prados A, 1993 Phys. Rev. E 47 1541  Brey J J and Prados A, 1994 Phys. Rev. B 49 984  Metropolis N C, Rosenbluth A W, Rosenbluth M N, Teller A H and Teller E, 1953 J. Chem. Phys. 21 1087  Newman M E J and Barkema G T, 1999 Monte Carlo Methods in Statistical Physics (Oxford: Oxford University Press)  Bender C M and Orszag S A, 1999 Advanced Mathematical Methods for Scientists and Engineers (New York: Springer)