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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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Related in: MedlinePlus

A schematic phase diagram of the Ising-like Heisenberg model in the coordinate (T,H), where HC1 = 3J, HC2 = , and HC1 = (6A + 3)J.
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fig10: A schematic phase diagram of the Ising-like Heisenberg model in the coordinate (T,H), where HC1 = 3J, HC2 = , and HC1 = (6A + 3)J.

Mentions: In the case of zero magnetic field, the system shows successive phase transitions when we change the temperature. At a high temperature TC1, the z component is ordered, and then at a low temperature TC2 the transverse component is ordered to form the distorted 120° structure61) as shown in Fig. 10 at H = 0. The former phase transition belongs to the universality classes of the six-state clock model, and the latter to that of the XY model. Both of them are of the Kosterlitz–Thouless type in two dimensions. In three dimensions, the phase transitions are of normal second order of the three dimensional XY universality class.62) This mechanism of successive phase transition gives an alternate scenario to that of Mekata model for the successive phase transitions of frustrated Ising-like models in the triangular lattice. Indeed successive phase transitions of this type were also found in experiments (VCl2,63) etc.).


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 the Ising-like Heisenberg model in the coordinate (T,H), where HC1 = 3J, HC2 = , and HC1 = (6A + 3)J.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig10: A schematic phase diagram of the Ising-like Heisenberg model in the coordinate (T,H), where HC1 = 3J, HC2 = , and HC1 = (6A + 3)J.
Mentions: In the case of zero magnetic field, the system shows successive phase transitions when we change the temperature. At a high temperature TC1, the z component is ordered, and then at a low temperature TC2 the transverse component is ordered to form the distorted 120° structure61) as shown in Fig. 10 at H = 0. The former phase transition belongs to the universality classes of the six-state clock model, and the latter to that of the XY model. Both of them are of the Kosterlitz–Thouless type in two dimensions. In three dimensions, the phase transitions are of normal second order of the three dimensional XY universality class.62) This mechanism of successive phase transition gives an alternate scenario to that of Mekata model for the successive phase transitions of frustrated Ising-like models in the triangular lattice. Indeed successive phase transitions of this type were also found in experiments (VCl2,63) etc.).

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