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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 schematic phase diagram of a weakly XY-like Heisenberg model in the field. D = 0.01.
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fig12: A schematic phase diagram of a weakly XY-like Heisenberg model in the field. D = 0.01.

Mentions: Because of the entropy effect, at finite temperatures, phases of the Y-shape structure (Fig. 9(b)), and of the up-up-down structure (Fig. 9(c)), and of the V-shape structure (Fig. 9(d)) appear.66) In systems with a weak XY anisotropy, the umbrella structure is energetically favorable. However, the thermal fluctuation still causes the structures of Figs. 9(b)–(d), and we have a very complicated phase diagram in the coordinate (T,H) as depicted in Fig. 12 where we used a single-ion type anisotropy model instead of the anisotropic coupling model [34][41]In the figure, we adopted a very small value of D = 0.01. If we use a larger value such as D = 0.1, the Y-shape structure disappears, while the V shape structure still remains.68)


Phase transition in spin systems with various types of fluctuations.

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

A schematic phase diagram of a weakly XY-like Heisenberg model in the field. D = 0.01.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig12: A schematic phase diagram of a weakly XY-like Heisenberg model in the field. D = 0.01.
Mentions: Because of the entropy effect, at finite temperatures, phases of the Y-shape structure (Fig. 9(b)), and of the up-up-down structure (Fig. 9(c)), and of the V-shape structure (Fig. 9(d)) appear.66) In systems with a weak XY anisotropy, the umbrella structure is energetically favorable. However, the thermal fluctuation still causes the structures of Figs. 9(b)–(d), and we have a very complicated phase diagram in the coordinate (T,H) as depicted in Fig. 12 where we used a single-ion type anisotropy model instead of the anisotropic coupling model [34][41]In the figure, we adopted a very small value of D = 0.01. If we use a larger value such as D = 0.1, the Y-shape structure disappears, while the V shape structure still remains.68)

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