Model Ising
Model Ising (Jerman: [ˈiːzɪŋ]), juga disebut sebagai model Lenz-Ising atau model Ising-Lenz, dinamai dari Ernst Ising dan Wilhelm Lenz, adalah model matematika feromagnetisme dalam mekanika statistika. Model ini terdiri dari variabel diskrit yang mewakili momen dipol magnetik dari "putaran" atom yang dapat berada di salah satu dari dua keadaan (+1 atau −1). Putaran diatur dalam grafik, biasanya kisi (di mana struktur lokal berulang secara berkala ke segala arah), memungkinkan setiap putaran berinteraksi dengan tetangganya. Putaran tetangga yang setuju memiliki energi lebih rendah daripada yang tidak setuju; sistem cenderung ke energi terendah tetapi panas mengganggu kecenderungan ini, sehingga menciptakan kemungkinan fase struktural yang berbeda. Model ini memungkinkan identifikasi perubahan wujud zat sebagai model realitas yang disederhanakan. Model Ising kisi persegi dua dimensi adalah salah satu model statistik paling sederhana untuk menunjukkan perubahan wujud zat.[1]
Model Ising ditemukan oleh fisikawan bernama Wilhelm Lenz (1920), yang memberikannya sebagai salash satu contoh masalah mekanika statistika kepada muridnya bernama Ernst Ising. Model Ising satu dimensi diselesaikan oleh (Ising 1925) dalam tesisnya tahun 1924;[2] model ini tidak memiliki perubahan wujud zat. Model Ising kisi persegi dua dimensi jauh lebih sulit dan hanya diberikan deskripsi secara analitis lama berselang, oleh Lars Onsager (1944). Biasanya diselesaikan dengan metode matriks transfer, meskipun ada pendekatan yang berbeda, lebih terkait dengan teori medan kuantum.
Dalam dimensi yang lebih besar dari empat, perubahan wujud zat model Ising dijelaskan oleh teori medan rata-rata.
Masalah Ising tanpa medan eksternal dapat dirumuskan secara ekuivalen sebagai masalah pemotongan maksimum graf yang dapat diselesaikan melalui optimasi kombinatorial.
Referensi
Catatan kaki
- ^ Lihat (Gallavotti 1999), Bab VI-VII.
- ^ Ernst Ising, Contribution to the Theory of Ferromagnetism
Daftar pustaka
- Baxter, Rodney J. (1982), Exactly solved models in statistical mechanics, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-083180-7, MR 0690578
- K. Binder (2001) [1994], "Ising model", dalam Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
- Brush, Stephen G. (1967). "History of the Lenz-Ising Model". Reviews of Modern Physics. 39 (4): 883–893. Bibcode:1967RvMP...39..883B. doi:10.1103/RevModPhys.39.883.
- Baierlein, R. (1999), Thermal Physics, Cambridge: Cambridge University Press, ISBN 978-0-521-59082-2
- Gallavotti, G. (1999), Statistical mechanics, Texts and Monographs in Physics, Berlin: Springer-Verlag, doi:10.1007/978-3-662-03952-6, ISBN 978-3-540-64883-3, MR 1707309
- Huang, Kerson (1987), Statistical mechanics (2nd edition), Wiley, ISBN 978-0-471-81518-1
- Ising, E. (1925), "Beitrag zur Theorie des Ferromagnetismus", Z. Phys., 31 (1): 253–258, Bibcode:1925ZPhy...31..253I, doi:10.1007/BF02980577, S2CID 122157319
- Itzykson, Claude; Drouffe, Jean-Michel (1989), Théorie statistique des champs, Volume 1, Savoirs actuels (CNRS), EDP Sciences Editions, ISBN 978-2-86883-360-0
- Itzykson, Claude; Drouffe, Jean-Michel (1989), Statistical field theory, Volume 1: From Brownian motion to renormalization and lattice gauge theory, Cambridge University Press, ISBN 978-0-521-40805-9
- Friedli, S.; Velenik, Y. (2017). Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction. Cambridge: Cambridge University Press. ISBN 9781107184824.
- Ross Kindermann and J. Laurie Snell (1980), Markov Random Fields and Their Applications. American Mathematical Society. ISBN 0-8218-3381-2.
- Kleinert, H (1989), Gauge Fields in Condensed Matter, Vol. I, "Superflow and Vortex Lines", pp. 1–742, Vol. II, "Stresses and Defects", pp. 743–1456, World Scientific (Singapore); Paperback ISBN 9971-5-0210-0 (also available online: Vol. I and Vol. II)
- Kleinert, H and Schulte-Frohlinde, V (2001), Critical Properties of φ4-Theories, World Scientific (Singapore); Paperback ISBN 981-02-4658-7 (also available online)
- Lenz, W. (1920), "Beiträge zum Verständnis der magnetischen Eigenschaften in festen Körpern", Physikalische Zeitschrift, 21: 613–615.
- Barry M. McCoy and Tai Tsun Wu (1973), The Two-Dimensional Ising Model. Harvard University Press, Cambridge Massachusetts, ISBN 0-674-91440-6
- Montroll, Elliott W.; Potts, Renfrey B.; Ward, John C. (1963), "Correlations and spontaneous magnetization of the two-dimensional Ising model", Journal of Mathematical Physics, 4 (2): 308–322, Bibcode:1963JMP.....4..308M, doi:10.1063/1.1703955, ISSN 0022-2488, MR 0148406, diarsipkan dari asli tanggal 2013-01-12
- Onsager, Lars (1944), "Crystal statistics. I. A two-dimensional model with an order-disorder transition", Physical Review, Series II, 65 (3–4): 117–149, Bibcode:1944PhRv...65..117O, doi:10.1103/PhysRev.65.117, MR 0010315
- Onsager, Lars (1949), "Discussion", Supplemento al Nuovo Cimento, 6: 261
- John Palmer (2007), Planar Ising Correlations. Birkhäuser, Boston, ISBN 978-0-8176-4248-8.
- Istrail, Sorin (2000), "Statistical mechanics, three-dimensionality and NP-completeness. I. Universality of intractability for the partition function of the Ising model across non-planar surfaces (extended abstract)" (PDF), Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, ACM, hlm. 87–96, doi:10.1145/335305.335316, ISBN 978-1581131840, MR 2114521, S2CID 7944336
- Yang, C. N. (1952), "The spontaneous magnetization of a two-dimensional Ising model", Physical Review, Series II, 85 (5): 808–816, Bibcode:1952PhRv...85..808Y, doi:10.1103/PhysRev.85.808, MR 0051740
Pranala luar
- Ising model at The Net Advance of Physics
- Barry Arthur Cipra, "The Ising model is NP-complete", SIAM News, Vol. 33, No. 6; online edition (.pdf)
- Science World article on the Ising Model
- A dynamical 2D Ising java applet oleh UCSC
- A dynamical 2D Ising java applet
- A larger/more complicated 2D Ising java applet
- Ising Model simulation oleh Enrique Zeleny, the Wolfram Demonstrations Project
- Phase transitions on lattices
- Three-dimensional proof for Ising Model impossible, Sandia researcher claims
- Interactive Monte Carlo simulation of the Ising, XY and Heisenberg models with 3D graphics(requires WebGL compatible browser)
- Ising Model code , image denoising example with Ising Model
- David Tong's Lecture Notes provide a good introduction
- The Cartoon Picture of Magnets That Has Transformed Science - Quanta Magazine article about Ising model
- Simulation of the 2-dimensional Ising model in Julia: https://github.com/cossio/SquareIsingModel.jl
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