Prados, A. and Bonilla, L.L. and Carpio Rodríguez, Ana María
(2010)
*Phase transitions in a mechanical system coupled to Glauber spins.*
Journal of Statistical Mechanics: Theory and Experiment
.
ISSN 1742-5468

PDF
Restricted to Repository staff only until 2020. 555kB |

Official URL: http://iopscience.iop.org/1742-5468/2010/06/P06016/pdf/1742-5468_2010_06_P06016.pdf

## 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 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.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Dimensional ising-model; DNA Denaturation; Dynamics classical phase transitions (theory); stochastic particle dynamics (theory); stochastic processes (theory) |

Subjects: | Sciences > Physics > Mathematical physics |

ID Code: | 14879 |

References: | [1] Boisen A, 2009 Nat. Nanotechnol. 4 404 [2] Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A and Zwerger W, 1987 Rev. Mod. Phys. 59 1 [3] Bonilla L L and Guinea F, 1992 Phys. Rev. A 45 7718 [4] Feder J and Pytte E, 1973 Phys. Rev. B 8 3978 [5] Rikvold P A, 1978 Z. Phys. B 30 339 [6] Hicke C and Dykman M I, 2008 Phys. Rev. B 78 024401 [7] Glauber R J, 1963 J. Math. Phys. 4 294 [8] Peyrard M, 2006 Nat. Phys. 2 13 [9] Dauxois T, Peyrard M and Bishop A R, 1993 Phys. Rev. E 47 684 [10] Wartell R M and Benight A S, 1985 Phys. Rep. 126 67 [11] Reiss H, 1980 Chem. Phys. 47 15 [12] Brey J J and Prados A, 1993 Physica A 197 569 [13] Brey J J and Prados A, 1996 Phys. Rev. E 53 458 [14] Van Kampen N G, 1997 Stochastic Processes in Physics and Chemistry (Amsterdam: North-Holland) [15] Reichl L E, 1998 A Modern Course in Statistical Physics (New York: Wiley) [16] Bragg W L and Williams E J, 1934 Proc. R. Soc. A 145 699 [17] Kafri Y, Mukamel D and Peliti L, 2000 Phys. Rev. Lett. 85 4988 [18] Hanke A, Ochoa M G and Metzler R, 2008 Phys. Rev. Lett. 100 018106 [19] Giaconi G and Toninelli F L, 2006 Phys. Rev. Lett. 96 070602 [20] Brey J J and Prados A, 1993 Phys. Rev. E 47 1541 [21] Brey J J and Prados A, 1994 Phys. Rev. B 49 984 [22] Metropolis N C, Rosenbluth A W, Rosenbluth M N, Teller A H and Teller E, 1953 J. Chem. Phys. 21 1087 [23] Newman M E J and Barkema G T, 1999 Monte Carlo Methods in Statistical Physics (Oxford: Oxford University Press) [24] Bender C M and Orszag S A, 1999 Advanced Mathematical Methods for Scientists and Engineers (New York: Springer) |

Deposited On: | 19 Apr 2012 08:37 |

Last Modified: | 06 Feb 2014 10:11 |

Repository Staff Only: item control page