Limits...
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.

Show MeSH

Related in: MedlinePlus

Temperature dependences of the specific heat (thin line) and of the spontaneous magnetization of the ferromagnetic two-dimensional Ising model [7] with H = 0.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3066537&req=5

fig01: Temperature dependences of the specific heat (thin line) and of the spontaneous magnetization of the ferromagnetic two-dimensional Ising model [7] with H = 0.

Mentions: As an example, we show the critical properties of the two-dimensional Ising model on the square lattice which is the most well-known and a prototype system for the phase transition:[7]where σ = ±1 and 〈ij〉 denotes all the nearest neighbor pairs on the lattice. In Fig. 1, we depict the specific heat obtained by Onsager3) by the thin curves. There, we see the divergence at the critical point .


Phase transition in spin systems with various types of fluctuations.

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

Temperature dependences of the specific heat (thin line) and of the spontaneous magnetization of the ferromagnetic two-dimensional Ising model [7] with H = 0.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig01: Temperature dependences of the specific heat (thin line) and of the spontaneous magnetization of the ferromagnetic two-dimensional Ising model [7] with H = 0.
Mentions: As an example, we show the critical properties of the two-dimensional Ising model on the square lattice which is the most well-known and a prototype system for the phase transition:[7]where σ = ±1 and 〈ij〉 denotes all the nearest neighbor pairs on the lattice. In Fig. 1, we depict the specific heat obtained by Onsager3) by the thin curves. There, we see the divergence at the critical point .

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