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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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Temperature dependence of the correlation function 〈σ1σ2〉=tanh(Keff(T)) of the decorated bond [29]. Inset shows the bond structure, where the circles denote the system spins σ1 and σ2, and the squares the decoration spins s1 and s2.
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fig07: Temperature dependence of the correlation function 〈σ1σ2〉=tanh(Keff(T)) of the decorated bond [29]. Inset shows the bond structure, where the circles denote the system spins σ1 and σ2, and the squares the decoration spins s1 and s2.

Mentions: Another interesting property of the frustrated systems is the non-monotonic ordering process due to the peculiar distribution of degeneracy. The non-monotonicity is understood by the idea of the decorated bond.46,47) A typical example of the decorated bond is depicted in Fig. 7. There, two spins, σ1 and σ2, which we call the system spin, are connected by a direct bond (J0) and two paths with the spins si (i = 1 and 2) which we call the decoration spin. The Hamiltonian of the decorated bond is given by[29]The effective interaction K(Teff) between the system spins is given by[30]where Z0 is a factor independent of σi. At high temperatures, because of the entropy effect, the contribution to the effective interaction through the decoration spins is weak (i.e., tanh-1(tanh2βJ1)\propto(βJ1)2). On the other hand, at low temperatures, the effective coupling constant is approximately given by the sum of interactions of all the three paths, i.e., K(T) ∼eq (2J1 − J0)/kBT.


Phase transition in spin systems with various types of fluctuations.

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

Temperature dependence of the correlation function 〈σ1σ2〉=tanh(Keff(T)) of the decorated bond [29]. Inset shows the bond structure, where the circles denote the system spins σ1 and σ2, and the squares the decoration spins s1 and s2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig07: Temperature dependence of the correlation function 〈σ1σ2〉=tanh(Keff(T)) of the decorated bond [29]. Inset shows the bond structure, where the circles denote the system spins σ1 and σ2, and the squares the decoration spins s1 and s2.
Mentions: Another interesting property of the frustrated systems is the non-monotonic ordering process due to the peculiar distribution of degeneracy. The non-monotonicity is understood by the idea of the decorated bond.46,47) A typical example of the decorated bond is depicted in Fig. 7. There, two spins, σ1 and σ2, which we call the system spin, are connected by a direct bond (J0) and two paths with the spins si (i = 1 and 2) which we call the decoration spin. The Hamiltonian of the decorated bond is given by[29]The effective interaction K(Teff) between the system spins is given by[30]where Z0 is a factor independent of σi. At high temperatures, because of the entropy effect, the contribution to the effective interaction through the decoration spins is weak (i.e., tanh-1(tanh2βJ1)\propto(βJ1)2). On the other hand, at low temperatures, the effective coupling constant is approximately given by the sum of interactions of all the three paths, i.e., K(T) ∼eq (2J1 − J0)/kBT.

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