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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 vortex configuration of the two-dimensional XY model [12] in a transient process of ordering. The open circles denote the ‘+’ vortices and the closed circles ‘−’ vortices.
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fig03: A vortex configuration of the two-dimensional XY model [12] in a transient process of ordering. The open circles denote the ‘+’ vortices and the closed circles ‘−’ vortices.

Mentions: Appearance of single vortex indicates the relevance of the periodicity, and thus it is a symbol of the high temperature phase. On the other hand, in the low temperature phase the interaction is so strong that configurations reflecting the periodicity of the angle cannot appear. Thus, at low temperatures, the periodicity of the angle is irrelevant. This fact is expressed by the absence of single vortex, which means essentially no vortex. However, at finite temperatures, thermal fluctuation may still cause the appearance of them in a form of pair of ‘±’ vortices which is localized in the space. This change from the free single vortices to the bounded pair vortices is called “vortex association” at the Kosterlitz–Thouless transition. In equilibrium configurations of the XY model, it is hard to identify vortices clearly. At high temperatures, configurations are too much disturbed to identify the vortices, and at low temperatures, the probability for well-recognize vortex pair is very low.20) In Fig. 3, we depict a typical configuration with vortices, where the ‘±’ vortices are shown by open and solid circles, respectively. It should be noted that this is a transient configuration from a random configuration to an aligned one at a low temperature.


Phase transition in spin systems with various types of fluctuations.

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

A vortex configuration of the two-dimensional XY model [12] in a transient process of ordering. The open circles denote the ‘+’ vortices and the closed circles ‘−’ vortices.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig03: A vortex configuration of the two-dimensional XY model [12] in a transient process of ordering. The open circles denote the ‘+’ vortices and the closed circles ‘−’ vortices.
Mentions: Appearance of single vortex indicates the relevance of the periodicity, and thus it is a symbol of the high temperature phase. On the other hand, in the low temperature phase the interaction is so strong that configurations reflecting the periodicity of the angle cannot appear. Thus, at low temperatures, the periodicity of the angle is irrelevant. This fact is expressed by the absence of single vortex, which means essentially no vortex. However, at finite temperatures, thermal fluctuation may still cause the appearance of them in a form of pair of ‘±’ vortices which is localized in the space. This change from the free single vortices to the bounded pair vortices is called “vortex association” at the Kosterlitz–Thouless transition. In equilibrium configurations of the XY model, it is hard to identify vortices clearly. At high temperatures, configurations are too much disturbed to identify the vortices, and at low temperatures, the probability for well-recognize vortex pair is very low.20) In Fig. 3, we depict a typical configuration with vortices, where the ‘±’ vortices are shown by open and solid circles, respectively. It should be noted that this is a transient configuration from a random configuration to an aligned one at a low temperature.

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