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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 snapshot of equilibrium spin configuration obtained by a Monte Carlo method near the critical point T = 2.3/J and H = 0 (cf. TC/J∼2.269…). The solid and open circles denote σi = 1 and σi = −1, respectively.
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fig02: A snapshot of equilibrium spin configuration obtained by a Monte Carlo method near the critical point T = 2.3/J and H = 0 (cf. TC/J∼2.269…). The solid and open circles denote σi = 1 and σi = −1, respectively.

Mentions: In Fig. 2, we plot a typical spin configuration near the critical temperature where we find large domains. The linear dimension of the domain corresponds to the correlation length ξ[9]where rij is the distance between the sites i and j, and η is the exponent so-called anomalous dimension. The divergence of the correlation length is expressed as[10]with ν = 1. It is known that the exponent η is 1/4 for the present model. At the critical point, fluctuation of the order parameter becomes large which results in the divergence of χ. Although the susceptibility has not yet been obtained analytically, it has been established that it diverges with the exponent γ = 7/4 of Eq. [4]. This divergence of χ corresponds to the correlation length ξ. The exponent ν is related to γ and η as[11]This is an example of the scaling relations among the critical exponents.16)


Phase transition in spin systems with various types of fluctuations.

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

A snapshot of equilibrium spin configuration obtained by a Monte Carlo method near the critical point T = 2.3/J and H = 0 (cf. TC/J∼2.269…). The solid and open circles denote σi = 1 and σi = −1, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig02: A snapshot of equilibrium spin configuration obtained by a Monte Carlo method near the critical point T = 2.3/J and H = 0 (cf. TC/J∼2.269…). The solid and open circles denote σi = 1 and σi = −1, respectively.
Mentions: In Fig. 2, we plot a typical spin configuration near the critical temperature where we find large domains. The linear dimension of the domain corresponds to the correlation length ξ[9]where rij is the distance between the sites i and j, and η is the exponent so-called anomalous dimension. The divergence of the correlation length is expressed as[10]with ν = 1. It is known that the exponent η is 1/4 for the present model. At the critical point, fluctuation of the order parameter becomes large which results in the divergence of χ. Although the susceptibility has not yet been obtained analytically, it has been established that it diverges with the exponent γ = 7/4 of Eq. [4]. This divergence of χ corresponds to the correlation length ξ. The exponent ν is related to γ and η as[11]This is an example of the scaling relations among the critical exponents.16)

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