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Roles of Quantum Fluctuation in Frustrated Systems – Order by Disorder and Reentrant Phase Transition

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Quantum Quenching, Annealing and Computation

Part of the book series: Lecture Notes in Physics ((LNP,volume 802))

Abstract

Frustration in systems shows many interesting equilibrium and dynamical properties [1–6]. In frustrated classical systems, there is no ground state where all the interactions are satisfied energetically. Because the ground states in regularly frustrated classical systems have many energetically unsatisfied interactions, there are many degenerated ground states and the residual entropy is larger than that of unfrustrated systems. Figure 10.1 shows the ground states of three Ising spins on antiferromagnetic triangle cluster. The closed and open circles in Fig. 10.1 denote up and down spins, respectively. The crosses in Fig. 10.1 represent energetically unsatisfied interactions.

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Acknowledgement

We thank Hans de Raedt, Bernard Barbara, Eric Vincent, Hiroshi Nakagawa, Kenichi Kurihara, Hosho Katsura, Issei Sato, and Yoshiki Matsuda for fruitful discussions. This work was partially supported by Research on Priority Areas “Physics of new quantum phases in superclean materials” (Grant No. 17071011) from MEXT, and also by the Next Generation Super Computer Project, Nanoscience Program from MEXT, The authors also thank the Supercomputer Center, Institute for Solid State Physics, University of Tokyo for the use of the facilities.

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Authors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha Kashiwa-shi, Chiba, Japan

    S. Tanaka

  2. Department of Physics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan

    M. Hirano & S. Miyashita

  3. CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama, 332-0012, Japan

    S. Miyashita

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  1. S. Tanaka
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  2. M. Hirano
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  3. S. Miyashita
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Correspondence to S. Tanaka , M. Hirano or S. Miyashita .

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  1. Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Bidhannagar 1/AF, Kolkata, 700064, India

    Anjan Kumar Chandra

  2. Theoretical Physics (ICTP), Abdus Salam International Centre for, Strada Costiera 11, Trieste, 34014, Italy

    Arnab Das

  3. Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Bidhannagar 1/AF, Kolkata, 700064, India

    Bikas K. Chakrabarti

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Tanaka, S., Hirano, M., Miyashita, S. (2010). Roles of Quantum Fluctuation in Frustrated Systems – Order by Disorder and Reentrant Phase Transition. In: Chandra, A., Das, A., Chakrabarti, B. (eds) Quantum Quenching, Annealing and Computation. Lecture Notes in Physics, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11470-0_10

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