The critical properties of magnetic system using generalized belief propagation technique

• Autorzy: Gwizdałła T.
• Konferencja: Evolutionary Computation and Global Optimization 2008 / National Conference (11 ; 2-4.06.2008 ; Szymbark, Poland)
• Języki publikacji: EN

Abstrakty

EN

Since few years the Belief Propagation [13, 14, 15] algorithm is reported as a very efficient tool to perform the optimization of systems which can be topologically transformed to the one of acceptable equivalent forms [9, 7]. The Ising system is often mentioned in these papers as a good example to present some basic foundations of BP. It is however rarely used as a tool to solve the Ising system itself. In this article we are going to present the analysis of critical properties, connected to the phase transition of magnetic system described by the Ising hamiltonian and the comparison of results to those obtained using evolutionary algorithm.

Słowa kluczowe

EN

Generalized Belief Propagation algorithm; GBP; evolutionary algorithm; EA; Ising model; hamiltonian; magnetic system

PL

algorytm ewolucyjny; model Isinga; hamiltonian; układ magnetyczny

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Elektronika
• Rocznik: 2008
• Tom: z. 165
• Strony: 85--93
• Opis fizyczny: Bibliogr. 15 poz., tab., rys., wykr.

Twórcy

autor

Gwizdałła T.

• University of Łódź, Dept. of Solid State Physics, Pomorska 149/153, 90-236 Łódź, Poland,

Bibliografia

• [1] Dirk Jan Bukman, Guozhong An, and J. M. J. van Leeuwen. Cluster-variation approach to the spin-1/2 xxz model. Phys. Rev. B, 43(16):13352-13364, Jun 1991.
• [2] L. Casetti and M. Kastner. Partial equivalence of statistical ensembles and kinetic energy. Physica A, 384:318, 2007.
• [3] T.M. Gwizdałła. Ising model studied using evolutionary approach. Mod. Phys. Lett. B, 19:169, 2005.
• [4] T.M. Gwizdałła. Magnetic problems as a benchmark for genetic algorithms operators. In Proceedings of X KAEiOG Conference, Bedlewo, pages 115-123, 2007.
• [5] R. Kikuchi. A theory of cooperative phenomena. Phys. Rev., 6:988-1003, 1981.
• [6] H. Meirovitch. Computer simulation study of hysteresis and free energy an the fcc Ising antiferromagnet. Phys. Rev. B, 30(5):2866-2874, 1984.
• [7] J.M. Mooij and H.J Kappen. On the properties of the Bethe approximation and loopy belief propagation on binary networks. J. Stat. Mech., 5:P11012, 2005.
• [8] L. Onsager. Crystal statistics. I. a two-dimensional model with an order-disorder transition. Phys. Rev., 65:117, 1944.
• [9] P. Pakzad and V. Anantharam. Minimal graphical representation of Kikuchi regions. In Proceedings of the Allerton Conference on Communication, Control, and Computing. Piscataway. IEEE, 2002.
• [10] J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, 1988.
• [11] A. Szarecka, R.P. White, and H. Meirovitch. Absolute entropy and free energy of fluids using the hypothetical scanning method. I. calculation of transition probabilities from local grand canonical partition functions. J. Chem. Phys., 119:12084-12095, 2003.
• [12] C. Tsallis. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 52:479-487, 1988.
• [13] J.S. Yedidia, W.T. Freeman, and Y. Weiss. Bethe free energy, Kikuchi approximations and belief propagation algorithms. In MERL Report, 2000.
• [14] J.S. Yedidia, W.T. Freeman, and Y. Weiss. Understanding belief propagation and its generalizations. In G. Lakemeyer and B. Nebel, editors, Exploring Artificial Intelligence in the New Millenium, pages 239-269. Morgan Kaufmann, 2003.
• [15] J.S. Yedidia, W.T. Freeman, and Y. Weiss. Constructing free-energy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory, 51:2282-2312, 2005.