Spin sistemlerinde rasgeleliğin faz geçişi üzerine etkilerinin incelenmesi
Investigation of the effects of randomness on phase transition in spin models
- Tez No: 97798
- Danışmanlar: PROF. DR. TARIK ÇELİK
- Tez Türü: Doktora
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2000
- Dil: Türkçe
- Üniversite: Hacettepe Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Fizik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 139
Özet
SUMMARY The understanding of the role played by impurities on nature of phase transi tion is of great importance, both from experimental and theoretical perspec tives. Although the effects of quenched bond randomness in pure systems which has continuous phase transition are well understood, it is not so clear what happens when randomness is introduced to systems undergoing a first- order phase transition. Phenomenological renormalization group arguments by Hui and Berker (1989) and rigorous proof of the vanishing of the latent heat by Aizenman and Wehr (1989) showed that bond randomness will induce a second-order phase tran sition. The renormalization group arguments state that any infinitesimal amount of bond randomness will drive the system to exhibit a second-order phase transition for d < 2 where d is the spatial dimensionality. The first Monte Carlo study of the effect of bond randomness has been done by Chen, Ferrenberg and Landau (1993). These authors studied the d = 2, 8 - state Potts model which,in pure case, exhibits strongly first-order phase tran sition. They showed that the transition becomes second-order in the presence of strong enough bond randomness of one chosen value. In these works the varying randomness is not addressed and the conversion of a first-order phase transition into a second-order one even for infinitesimal randomness is not yet established. It would be quite relevant to study the changes in characteristic behaviors of the system with respect to the introduction of a gradually increasing degree of bond randomness as well as its finite size dependence. The main objective of this work is to understand the effect of quenched bond randomness on the transition and correlation between the amount of randomness and finite sizeVI of the system by consecutive increases of quenched randomness and deduce the interplay of finite size and strength of randomness crossover. We first investigated the threshold value of the two-dimensional 8-state Potts model with varying bond randomness for different lattice sizes. The model is studied by a highly convincing method of Monte Carlo simulations using Swendsen-Wang cluster algorithm. For arbitrarily chosen varying amounts of bond randomness, we observed the energy and the average cluster size his tograms as well as specific heat, Binder cumulant and the energy-time sequence in order to gain insight into the order of phase transition existing in the system. Secondly, we considered the autocorrelation times and showed that by mon itoring the autocorrelation times one can trace down the threshold value of the introduced quenched bond randomness for the rounding of the first-order phase transition. We have also studied the influence of the distribution of bimodal bonds over the lattice on the phase transition. The effects of the periodic and random distributions of bonds are compared and the importance of randomness is demonstrated.
Özet (Çeviri)
SUMMARY The understanding of the role played by impurities on nature of phase transi tion is of great importance, both from experimental and theoretical perspec tives. Although the effects of quenched bond randomness in pure systems which has continuous phase transition are well understood, it is not so clear what happens when randomness is introduced to systems undergoing a first- order phase transition. Phenomenological renormalization group arguments by Hui and Berker (1989) and rigorous proof of the vanishing of the latent heat by Aizenman and Wehr (1989) showed that bond randomness will induce a second-order phase tran sition. The renormalization group arguments state that any infinitesimal amount of bond randomness will drive the system to exhibit a second-order phase transition for d < 2 where d is the spatial dimensionality. The first Monte Carlo study of the effect of bond randomness has been done by Chen, Ferrenberg and Landau (1993). These authors studied the d = 2, 8 - state Potts model which,in pure case, exhibits strongly first-order phase tran sition. They showed that the transition becomes second-order in the presence of strong enough bond randomness of one chosen value. In these works the varying randomness is not addressed and the conversion of a first-order phase transition into a second-order one even for infinitesimal randomness is not yet established. It would be quite relevant to study the changes in characteristic behaviors of the system with respect to the introduction of a gradually increasing degree of bond randomness as well as its finite size dependence. The main objective of this work is to understand the effect of quenched bond randomness on the transition and correlation between the amount of randomness and finite sizeVI of the system by consecutive increases of quenched randomness and deduce the interplay of finite size and strength of randomness crossover. We first investigated the threshold value of the two-dimensional 8-state Potts model with varying bond randomness for different lattice sizes. The model is studied by a highly convincing method of Monte Carlo simulations using Swendsen-Wang cluster algorithm. For arbitrarily chosen varying amounts of bond randomness, we observed the energy and the average cluster size his tograms as well as specific heat, Binder cumulant and the energy-time sequence in order to gain insight into the order of phase transition existing in the system. Secondly, we considered the autocorrelation times and showed that by mon itoring the autocorrelation times one can trace down the threshold value of the introduced quenched bond randomness for the rounding of the first-order phase transition. We have also studied the influence of the distribution of bimodal bonds over the lattice on the phase transition. The effects of the periodic and random distributions of bonds are compared and the importance of randomness is demonstrated.
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