The Efficiency of Transfer-matrix Simulations of Supramolecular Magnets in the Parallel Computing Environment
Matysiak Ryszard, Kamieniarz Grzegorz
Institute of Engineering and Computer Education, University of Zielona Góra
ul. prof. Z. Szafrana 4, 65-516 Zielona Góra, Poland
r.matysiak@eti.uz.zgora.pl
Computational Physics Division, Institute of Physics, Adam Mickiewicz University
ul. Umultowska 85, 61-614 Poznań, Poland
gjk@amu.edu.pl
Received:
Rec. 11 November 2005
DOI: 10.12921/cmst.2006.12.02.139-142
OAI: oai:lib.psnc.pl:621
Abstract:
The deterministic quantum transfer-matrix (QTM) technique and its mathematical background are presented. This important tool in computational physics can be applied to a class of the real physical low-dimensional magnetic systems described by the Heisenberg hamiltonian which includes the macroscopic molecular-based spin chains, small size magnetic clusters embedded in some supramolecules and other interesting compounds. In order to convert existing application for the susceptibility calculations to run on the grid, the speed-up and efficiency of parallelization are analyzed on the SGI Origin 3800 platform with p = 128 processor units. Using Message Parallel Interface (MPI) system libraries we find the efficiency of the code of 94% for p = 128 that makes our application suitable for the grid.
Key words:
Message Parallel Interface, quantum transfer-matrix technique
References:
[1] G. Kamieniarz and R. Matysiak, Comp. Mat. Sci. 28, 353 (2003).
[2] G. Kamieniarz, Phase Transitions 57, 105 (1996).
[3] D. Gatteschi, A. Caneschi, L. Pardi and R. Sessoli, Science 265, 1054 (1994).
[4] A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M. A. Novak, C. Paulsen and W. Wernsdorfer, J. Magn. Magn. Mat. 200, 182 (1999).
[5] D. Gatteschi, R. Sessoli and A. Cornia, J. Chem. Soc., Chem. Commun. 725 (2000).
[6] S. G. Louie, Nature 384, 612 (1996).
[7] T. Delica and H. Leschke, Physica A176, 736 (1990).
[8] H. Andres et al.: Chem. Eur. J. 21 4867 (2002).
[9] E. F. Van de Velde, Concurrent Scientific Computing, Springer-Verlag New York, Inc. (1994).
[10] J. Błażewicz, J. Kaczmarek, M. Kasprzak and J. Węglarz, Computational Methods in Science and Technology 1, 31 (1996).
[11] A. Caneschi, D. Gatteschi, J. Laugier, P. Rey, R. Sessoli, and C. Zanchini, J. Am. Chem. Soc. 110, 2795 (1988).
The deterministic quantum transfer-matrix (QTM) technique and its mathematical background are presented. This important tool in computational physics can be applied to a class of the real physical low-dimensional magnetic systems described by the Heisenberg hamiltonian which includes the macroscopic molecular-based spin chains, small size magnetic clusters embedded in some supramolecules and other interesting compounds. In order to convert existing application for the susceptibility calculations to run on the grid, the speed-up and efficiency of parallelization are analyzed on the SGI Origin 3800 platform with p = 128 processor units. Using Message Parallel Interface (MPI) system libraries we find the efficiency of the code of 94% for p = 128 that makes our application suitable for the grid.
Key words:
Message Parallel Interface, quantum transfer-matrix technique
References:
[1] G. Kamieniarz and R. Matysiak, Comp. Mat. Sci. 28, 353 (2003).
[2] G. Kamieniarz, Phase Transitions 57, 105 (1996).
[3] D. Gatteschi, A. Caneschi, L. Pardi and R. Sessoli, Science 265, 1054 (1994).
[4] A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M. A. Novak, C. Paulsen and W. Wernsdorfer, J. Magn. Magn. Mat. 200, 182 (1999).
[5] D. Gatteschi, R. Sessoli and A. Cornia, J. Chem. Soc., Chem. Commun. 725 (2000).
[6] S. G. Louie, Nature 384, 612 (1996).
[7] T. Delica and H. Leschke, Physica A176, 736 (1990).
[8] H. Andres et al.: Chem. Eur. J. 21 4867 (2002).
[9] E. F. Van de Velde, Concurrent Scientific Computing, Springer-Verlag New York, Inc. (1994).
[10] J. Błażewicz, J. Kaczmarek, M. Kasprzak and J. Węglarz, Computational Methods in Science and Technology 1, 31 (1996).
[11] A. Caneschi, D. Gatteschi, J. Laugier, P. Rey, R. Sessoli, and C. Zanchini, J. Am. Chem. Soc. 110, 2795 (1988).
