Phase transitions in a mechanical system coupled to Glauber spins

dc.contributor.authorPrados, A.
dc.contributor.authorBonilla, L.L.
dc.contributor.authorCarpio, Ana
dc.description.abstractA 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.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
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dc.journal.titleJournal of Statistical Mechanics: Theory and Experiment
dc.publisherIOP Publishing
dc.rights.accessRightsrestricted access
dc.subject.keywordDimensional ising-model
dc.subject.keywordDNA Denaturation
dc.subject.keywordDynamics classical phase transitions (theory)
dc.subject.keywordstochastic particle dynamics (theory)
dc.subject.keywordstochastic processes (theory)
dc.subject.ucmFísica matemática
dc.titlePhase transitions in a mechanical system coupled to Glauber spins
dc.typejournal article
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