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Phase transition in spin systems with various types of fluctuations.

Miyashita S - Proc. Jpn. Acad., Ser. B, Phys. Biol. Sci. (2010)

Bottom Line: Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance.As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established.However, we still find variety of features of ordering processes.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, The University of Tokyo, Japan. miya@spin.phys.s.u-tokyo.ac.jp

ABSTRACT
Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems.

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A diluted configuration with site occupation probability p = 0.5 which is below the critical probability of the percolation.
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fig14: A diluted configuration with site occupation probability p = 0.5 which is below the critical probability of the percolation.

Mentions: In the diluted ferromagnet, the domains are well defined. When dilution probability p exceeds the critical percolation concentration pC,94) the lattice is separated into finite domains with probability one. In Fig. 14, we depict a snap shot of a lattice of site dilution with p = 0.5 which is above pC for the square lattice with nearest neighbor interaction. We find finite clusters on it. In this case, we expect paramagnetic behavior. However, it has been pointed out that randomly diluted ferromagnets have a non-analytic free energy below the critical temperature of the non-diluted system. Although the probability for large clusters is very small, there is a non-vanishing probability to find arbitrarily large clusters for any p, which causes the non-analytic effect on the free energy. While it has little effect on the equilibrium properties, it has significant effect on the dynamics. For example, the autocorrelation function of spin is affected by the very long relaxation time of the large clusters at the temperature below the critical temperature of the pure system (p = 0), and shows a slow relaxation than the simple exponential decay. This type of slow relaxation is called dynamical effect of the Griffiths singularity.95,96)


Phase transition in spin systems with various types of fluctuations.

Miyashita S - Proc. Jpn. Acad., Ser. B, Phys. Biol. Sci. (2010)

A diluted configuration with site occupation probability p = 0.5 which is below the critical probability of the percolation.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3066537&req=5

fig14: A diluted configuration with site occupation probability p = 0.5 which is below the critical probability of the percolation.
Mentions: In the diluted ferromagnet, the domains are well defined. When dilution probability p exceeds the critical percolation concentration pC,94) the lattice is separated into finite domains with probability one. In Fig. 14, we depict a snap shot of a lattice of site dilution with p = 0.5 which is above pC for the square lattice with nearest neighbor interaction. We find finite clusters on it. In this case, we expect paramagnetic behavior. However, it has been pointed out that randomly diluted ferromagnets have a non-analytic free energy below the critical temperature of the non-diluted system. Although the probability for large clusters is very small, there is a non-vanishing probability to find arbitrarily large clusters for any p, which causes the non-analytic effect on the free energy. While it has little effect on the equilibrium properties, it has significant effect on the dynamics. For example, the autocorrelation function of spin is affected by the very long relaxation time of the large clusters at the temperature below the critical temperature of the pure system (p = 0), and shows a slow relaxation than the simple exponential decay. This type of slow relaxation is called dynamical effect of the Griffiths singularity.95,96)

Bottom Line: Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance.As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established.However, we still find variety of features of ordering processes.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, The University of Tokyo, Japan. miya@spin.phys.s.u-tokyo.ac.jp

ABSTRACT
Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems.

Show MeSH
Related in: MedlinePlus