Modeling and Simulations of Complex Low- Dimensional systems: Testing the Efficiency of Parallelization
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 molecularbased
spin chains, small size magnetic clusters embedded in some
supramolecules and other interesting compounds. Using QTM, the
spin degrees of freedom are accurately taken into account, yielding
the thermodynamical functions at finite temperatures.
In order to test the application for the susceptibility calculations to
run in the parallel environment, the speed-up and efficiency of
parallelization are analyzed on our platform SGI Origin 3800 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 highly scalable.
[1] G. Kamieniarz, and R. Matysiak, "Simulations of the low-dimensional
magnetic systems by the quantum transfer-matrix technique", Comp.
Mat. Sci., vol. 28, 2003, pp. 353-365.
[2] G. Kamieniarz, "Computer simulation studies of phase transitions and
low-dimensional magnets", Phase Transitions, vol. 57, 1996, pp. 105-
117.
[3] D. Gatteschi, A. Caneschi, and L. Pardi, and R. Sessoli, "Large clusters
of metal ions: the transition from molecular to bulk magnets", Science,
vol. 265, 1994, pp. 1054-1058.
[4] A. Caneschi, D., Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A.
Cornia, M.A. Novak, C. Paulsen, and W. Wernsdorfer, "The molecular
approach to nanoscale magnetism", J. Magn. Magn. Mat., vol. 200,
1999, pp. 182-201.
[5] D. Gatteschi, R. Sessoli, and A. Cornia, "Single-molecule magnets based
on iron(III) oxo clusters", J. Chem. Soc., Chem. Commun., 2000, (9),
725-732.
[6] S.G. Louie, "Nanoparticles behaving oddly", Nature, vol. 384, 1996, pp.
612-613.
[7] T. Delica, and H. Leschke, "Formulation and numerical results of the
transfer-matrix method for quantum spin chains", Physica, vol. A168,
1990, 736-767.
[8] A. Caneschi, D. Gatteschi, J. Laugier, P. Rey, R. Sessoli, and C.
Zanchini, "Preparation, crystal structure and magnetic properties of an
oligonuclear complex with with 12 coupled spins and S=12 ground
state", J. Am. Chem. Soc., vol. 110, 1988, pp. 2795-2799.
[9] H. Andres, R. Basler, A.J. Blake, C. Cadiou, G. Chaboussant, C.M.
Grant, H.-U. Guedel, M. Murrie, S. Parsons, C. Paulsen, F. Semandini,
V. Villar, W. Wensdorfer, and R.E.P. Winpenny, "Studies of a Nickle-
Based Single-Molecule Magnet", Chem. - Eur. J., vol. 8, 2002, pp.
5165-5172.
[10] E.F. Van de Velde, Concurrent Scientific Computing, Springer-Verlag
New York, Inc. ,1994.
[11] J. Blazewicz, J. Kaczmarek, M. Kasprzak, and J. Weglarz, "Sequential
algorithms for DNA sequencing", Comp. Methods Sci.Technol., vol. 1,
1996, pp. 31-42.
[1] G. Kamieniarz, and R. Matysiak, "Simulations of the low-dimensional
magnetic systems by the quantum transfer-matrix technique", Comp.
Mat. Sci., vol. 28, 2003, pp. 353-365.
[2] G. Kamieniarz, "Computer simulation studies of phase transitions and
low-dimensional magnets", Phase Transitions, vol. 57, 1996, pp. 105-
117.
[3] D. Gatteschi, A. Caneschi, and L. Pardi, and R. Sessoli, "Large clusters
of metal ions: the transition from molecular to bulk magnets", Science,
vol. 265, 1994, pp. 1054-1058.
[4] A. Caneschi, D., Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A.
Cornia, M.A. Novak, C. Paulsen, and W. Wernsdorfer, "The molecular
approach to nanoscale magnetism", J. Magn. Magn. Mat., vol. 200,
1999, pp. 182-201.
[5] D. Gatteschi, R. Sessoli, and A. Cornia, "Single-molecule magnets based
on iron(III) oxo clusters", J. Chem. Soc., Chem. Commun., 2000, (9),
725-732.
[6] S.G. Louie, "Nanoparticles behaving oddly", Nature, vol. 384, 1996, pp.
612-613.
[7] T. Delica, and H. Leschke, "Formulation and numerical results of the
transfer-matrix method for quantum spin chains", Physica, vol. A168,
1990, 736-767.
[8] A. Caneschi, D. Gatteschi, J. Laugier, P. Rey, R. Sessoli, and C.
Zanchini, "Preparation, crystal structure and magnetic properties of an
oligonuclear complex with with 12 coupled spins and S=12 ground
state", J. Am. Chem. Soc., vol. 110, 1988, pp. 2795-2799.
[9] H. Andres, R. Basler, A.J. Blake, C. Cadiou, G. Chaboussant, C.M.
Grant, H.-U. Guedel, M. Murrie, S. Parsons, C. Paulsen, F. Semandini,
V. Villar, W. Wensdorfer, and R.E.P. Winpenny, "Studies of a Nickle-
Based Single-Molecule Magnet", Chem. - Eur. J., vol. 8, 2002, pp.
5165-5172.
[10] E.F. Van de Velde, Concurrent Scientific Computing, Springer-Verlag
New York, Inc. ,1994.
[11] J. Blazewicz, J. Kaczmarek, M. Kasprzak, and J. Weglarz, "Sequential
algorithms for DNA sequencing", Comp. Methods Sci.Technol., vol. 1,
1996, pp. 31-42.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50982", author = "Ryszard Matysiak and Grzegorz Kamieniarz", title = "Modeling and Simulations of Complex Low- Dimensional systems: Testing the Efficiency of Parallelization", 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 molecularbased
spin chains, small size magnetic clusters embedded in some
supramolecules and other interesting compounds. Using QTM, the
spin degrees of freedom are accurately taken into account, yielding
the thermodynamical functions at finite temperatures.
In order to test the application for the susceptibility calculations to
run in the parallel environment, the speed-up and efficiency of
parallelization are analyzed on our platform SGI Origin 3800 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 highly scalable.", keywords = "Deterministic simulations, low-dimensional
magnets, modeling of complex systems, parallelization.", volume = "1", number = "11", pages = "514-4", }