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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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Phase diagram of the ordering patterns fHS(T) in the coordinate (D/zJ,\lng). Ordering patterns for various values of D: (Type I) smooth change for D > DC, (Type II) smooth change and a metastable branch at low temperatures for D > DC1 and D < DC2, (Type III) discontinuous change for DC1 > D > DC2, (Type IV) discontinuous change and a metastable branch at low temperatures for DC1 > D and D < DC2, and (Type V) HS is always stable or metastable for D < DC3.
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fig18: Phase diagram of the ordering patterns fHS(T) in the coordinate (D/zJ,\lng). Ordering patterns for various values of D: (Type I) smooth change for D > DC, (Type II) smooth change and a metastable branch at low temperatures for D > DC1 and D < DC2, (Type III) discontinuous change for DC1 > D > DC2, (Type IV) discontinuous change and a metastable branch at low temperatures for DC1 > D and D < DC2, and (Type V) HS is always stable or metastable for D < DC3.

Mentions: In Fig. 18, types of ordering processes corresponding the lines (I–V), and the phase diagram in the coordinate (\lng,D/zJ) are depicted.124,125) We find that the type IV appears for all the sequences in the parameter space. We call this feature “generic sequence of the temperature dependence of ordering fHS(T)”. We found this type of sequence also appears in the change of other parameters such as the pressure and stiffness of the elastic constant.


Phase transition in spin systems with various types of fluctuations.

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

Phase diagram of the ordering patterns fHS(T) in the coordinate (D/zJ,\lng). Ordering patterns for various values of D: (Type I) smooth change for D > DC, (Type II) smooth change and a metastable branch at low temperatures for D > DC1 and D < DC2, (Type III) discontinuous change for DC1 > D > DC2, (Type IV) discontinuous change and a metastable branch at low temperatures for DC1 > D and D < DC2, and (Type V) HS is always stable or metastable for D < DC3.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig18: Phase diagram of the ordering patterns fHS(T) in the coordinate (D/zJ,\lng). Ordering patterns for various values of D: (Type I) smooth change for D > DC, (Type II) smooth change and a metastable branch at low temperatures for D > DC1 and D < DC2, (Type III) discontinuous change for DC1 > D > DC2, (Type IV) discontinuous change and a metastable branch at low temperatures for DC1 > D and D < DC2, and (Type V) HS is always stable or metastable for D < DC3.
Mentions: In Fig. 18, types of ordering processes corresponding the lines (I–V), and the phase diagram in the coordinate (\lng,D/zJ) are depicted.124,125) We find that the type IV appears for all the sequences in the parameter space. We call this feature “generic sequence of the temperature dependence of ordering fHS(T)”. We found this type of sequence also appears in the change of other parameters such as the pressure and stiffness of the elastic constant.

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