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Phase Transitions in Long-range Spin Models: The Power of Generalized Ensembles

Abstract : This thesis uses generalized ensembles Monte Carlo methods to explore the critical behavior of spin chains with algebraically decaying interactions. The first part of this thesis investigates the phase diagram of a long-range Potts chain using a multicanonical algorithm. A new method based on spinodal points is proposed to detect the order of phase transitions. The boundary between first- and second-order transitions is located with unprecedented accuracy using this method, and a new, unusual finite-size effect is observed. The second part of this thesis formulates a new, versatile multicanonical method that includes cluster updates, considerably extending the range of attainable lattice sizes. The method is shown to be far more accurate than standard multicanonical methods. It is applied to the investigation of finite-size effects at first-order transitions, where strong evidence suggests that the mixed-phase configuration has a fractal dimension depending on the decay parameter of the interaction. Finally, a long-range Ising chain with bimodal random fields is studied. The existence of a tricritical point for slowly decaying interactions is demonstrated.
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Contributor : Sylvain Reynal <>
Submitted on : Friday, September 23, 2005 - 1:52:18 AM
Last modification on : Wednesday, December 2, 2020 - 4:20:07 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:43:38 PM


  • HAL Id : tel-00010256, version 1



Sylvain Reynal. Phase Transitions in Long-range Spin Models: The Power of Generalized Ensembles. Data Analysis, Statistics and Probability []. Université de Cergy Pontoise, 2005. English. ⟨tel-00010256⟩



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