Browsing by Subject "Ising model"
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Item Open Access Dynamic critical index of the Swendsen-Wang algorithm by dynamic finite-size scaling(Elsevier B.V., 2006-10-15) Dilaver, M.; Gündüç, S.; Aydin, M.; Gündüç, Y.In this work we have considered the dynamic scaling relation of the magnetization in order to study the dynamic scaling behavior of 2- and 3-dimensional Ising models. We have used the literature values of the magnetic critical exponents to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. In this way we have calculated the dynamic critical exponent Z for 2- and 3-dimensional Ising Models by using the Swendsen-Wang cluster algorithm. We have also presented that this method opens the possibility of calculating z and x(0) separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.Item Open Access Gibbs measures and phase transitions in various one-dimensional models(Bilkent University, 2013) Şensoy, AhmetIn the thesis, limiting Gibbs measures of some one dimensional models are investigated and various criterions for the uniqueness of limiting Gibbs states are considered. The criterion for models with unique ground state formulated in terms of percolation theory is presented and some applications of this criterion are discussed. A one-dimensional long range Widom-Rowlinson model with periodic and biased particle activities is explored. It is shown that if the spin interactions are sufficiently large versus particle activities then the Widom-Rowlinson model does not exhibit a phase transition at low temperatures. Finally, an interdisciplinary approach is followed. A financial application of the theory of phase transition is considered by applying the Ising model to understand the role of herd behavior on stock market crashes. Accordingly, model suggests a criteria to detect the existence of herd behavior in financial markets under certain assumptions.Item Open Access Phase transitions in tetrahedral Ising lattices(Bilkent University, 1993) Kabakçıoğlu, AlkanAfter a review of the Renormalization CJroup theory, the phase diagram of unisotro])ic tetrahedral Ising lattice is explored l)y the motivation gained through the recent experimental findings about SiGe alloys. Renormalization Group approcich and the mean-field R(J approximation previously pro])osed by Kinzel ¿ire used. Four different ordered pluises are olxserved. The critical expoiKMit // is Ciih’uhited using the liiUNirized t.ra.nsformItem Open Access Stepwise Positional-Orientational Order and the Multicritical-Multistructural Global Phase Diagram of the s=3/2 Ising Model From Renormalization-Group Theory(American Physical Society, 2016) Yunus, Ç.; Renklioǧlu, B.; Keskin, M.; Berker, A. N.The spin-32 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.