Phase Transitions in Long-range Spin Models: The Power of Generalized Ensembles
Year: 2005
Type: dissertation
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.
Source: HAL
Author: Sylvain Reynal
Institution: Laboratoire de Physique Théorique et Modélisation
Language: French
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W374099717