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Parallel Tempering Monte Carlo Simulations of Spherical Fixed-Connectivity Model for Polymerized Membranes

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Abstract

We study the first order phase transition of the fixed-connectivity triangulated surface model using the Parallel Tempering Monte Carlo (PTMC) technique on relatively large lattices. From the PTMC results, we find that the transition is considerably stronger than the reported ones predicted by the conventional Metropolis MC (MMC) technique and the flat histogram MC technique. We also confirm that the results of the PTMC on relatively smaller lattices are in good agreement with those known results. This implies that the PTMC is successfully used to simulate the first order phase transitions. The parallel computation in the PTMC is implemented by OpenMP, where the speed of the PTMC on multi-core CPUs is considerably faster than that on the single-core CPUs.

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Notes

  1. See documents for Intel Parallel Studio\(^{\textregistered }\), for example.

  2. The symbol D is used here for the spatial dimension instead of d to distinguish it from the dimension \(d(=\!3)\) of the external space \(\mathbf{R}^d\).

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Acknowledgments

We are grateful to Prof. Hideo Sekino for the support of the Promotion of Joint Research 2014, Toyohashi University of Technology. This work is supported in part by the Grant-in-Aid for Scientific Research (C) Number 26390138.

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Authors and Affiliations

  1. Advanced Course of Mechanical Engineering, National Institute of Technology Ibaraki College, Nakane 866, Hitachinaka, Ibaraki, 312-8508, Japan

    Satoshi Usui

  2. Department of Mechanical and Systems Engineering, National Institute of Technology Ibaraki College, Nakane 866, Hitachinaka, Ibaraki, 312-8508, Japan

    Hiroshi Koibuchi

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  1. Satoshi Usui
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  2. Hiroshi Koibuchi
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Correspondence to Hiroshi Koibuchi.

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Usui, S., Koibuchi, H. Parallel Tempering Monte Carlo Simulations of Spherical Fixed-Connectivity Model for Polymerized Membranes. J Stat Phys 162, 701–711 (2016). https://doi.org/10.1007/s10955-015-1428-1

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