An Introduction to the Ising Model

REFERENCES

• R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, 1982.
   Google Scholar
• N. L. Biggs, Interaction Models, Cambridge University Press, 1977.
   Google Scholar
• A. B. Bortz, Proofs of Spontaneous Magnetization Using the Peierls Method, Am. J. Phys., 40 (1972) 1524–1528.
   Web of Science ®Google Scholar
• S. G. Brush, History of the Lenz-Ising Model, Rev. Mod. Phys., 39 (1967) 883–893.
   Web of Science ®Google Scholar
• S. G. Brush, Statistical Physics and the Atomic Theory of Matter, from Boyle and Newton to Landau and Onsager, Princeton University Press, 1983.
   Google Scholar
• J. C. Dash, Two-Dimensional Matter, Scientific American, 228 (1973) 30–40.
   Web of Science ®Google Scholar
• R. L. Dobrushin, The existence of a phase transition in the two- and three-dimensional Ising models, Theory Prob. Appl. 10 (1965) 193–213.
   Web of Science ®Google Scholar
• C. Domb, Series Expansions for Ferromagnetic Models, Adv. Phys., 19 (1970) 339–370.
   Web of Science ®Google Scholar
• C. Domb and M. S. Green, eds., Phase Transitions and Critical Phenomena, Academic Press, vols. 1–6, 1972–1976.
   Google Scholar
• F. J. Dyson, Existence and Nature of Phase Transitions in One-Dimensional Ising Ferromagnets, in Mathematical Aspects of Statistical Mechanics (SIAM-AMS Proc. vol. 5, J. C. T. Poole, ed), AMS, 1972.
   Google Scholar
• R. Ellis, Entropy, Large Deviations, and Statistical Mechanics, Springer-Verlag, 1985.
   Google Scholar
• R. P. Feynman, Statistical Mechanics, Benjamin, 1972.
   Google Scholar
• M. E. Fisher, Simple Ising Models Still Thrive, Physica 106A (1981), 28–47.
   Google Scholar
• J. Frohlich, On the Mathematics of Phase Transitions and Critical Phenomena, in Proc. of the International Congress of Mathematicians, Helsinki (1978), 896–904.
   Google Scholar
• M. L. Glasser, Exact Partition Function for the Two-Dimensional Ising Model, Am. J. Phys., 38 (1970) 1033–1036.
   Web of Science ®Google Scholar
• R. B. Griffiths, Peierls' proof of spontaneous magnetization in a two-dimensional Ising ferromagnet, Phys. Rev. 136A (1964), 437–439.
   Google Scholar
• F. Harary, ed., Graph Theory and Theoretical Physics, Academic Press, 1967.
   Google Scholar
• E. Ising, Beitrag zur Theorie des Ferromagnetismus, Z. Physik, 31 (1925) 253–258.
   Web of Science ®Google Scholar
• M. Kac, Enigmas of Chance, Harper-Row, 1985.
   Google Scholar
• M. Kac, Phase Transitions, in The Physicist's Conception of Nature (J. Mehra, ed.), Reidel (1973) 814–826.
   Google Scholar
• M. Kac, Probability in Classical Physics, in Proc. of Symposia in Applied Mathematics, vol. 7, AMS (1957) 73–86.
   Google Scholar
• M. Kac and J. C. Ward, A Combinatorial Solution of the Two Dimensional Ising Model, Phys. Rev. 88 (1952) 1332–1337.
   Web of Science ®Google Scholar
• B. Kaufman and L. Onsager, Crystal Statistics II. Partition Function Evaluated by Spinor Analysis, Phys. Rev., 76 (1949) 1232–1243.
   Web of Science ®Google Scholar
• B. Kaufman and L. Onsager, Crystal Statistics III. Short-Range Order in a Binary Ising Model, Phys. Rev., 76 (1949) 1244–1252.
   Web of Science ®Google Scholar
• J. B. Kogut, An Introduction to Lattice Gauge Theory and Spin Systems, Rev. Mod. Phys., 51 (1979) 659–713.
   Web of Science ®Google Scholar
• H. A. Kramers and G. H. Wannier, Statistics of the two-dimensional ferromagnet, I and II, Phys. Rev., 60 (1941) 252–262, 263–276.
   Google Scholar
• L. D. Landau and E. M. Lifshitz, Statistical Physics, Pergamon Press, 1980.
   Google Scholar
• T. D. Lee and C. N. Yang, Statistical Theory of Equations of State and Phase Transitions I. Theory of Condensation, Phys. Rev., 87 (1952) 404–409.
   Web of Science ®Google Scholar
• T. D. Lee and C. N. Yang, Statistical Theory of Equations of State and Phase Transitions II. Lattice Gas and the Ising Model, Phys. Rev., 87 (1952) 410–419.
   Web of Science ®Google Scholar
• W. Lenz, Beitrag zum Verständnis der magnetishen Erscheinungen in festen Körpern, Z. Physik 21 (1920), 613–615.
   Google Scholar
• T. M. Ligget, Interacting Particle Systems, Springer-Verlag, 1985.
   Google Scholar
• S.-K. Ma, Statistical Mechanics, World Scientific, 1985.
   Google Scholar
• B. M. McCoy and T. T. Wu, The Two-Dimensional Ising Model, Harvard University Press, 1973.
   Google Scholar
• O. G. Mouritsen, Computer Studies of Phase Transitions and Critical Phenomena, Springer-Verlag, 1984
   Google Scholar
• G. F. Newell and E. W. Montroll, On the theory of the Ising Model of Ferromagnetism, Rev. Mod. Phys., 25 (1953) 353–389.
   Web of Science ®Google Scholar
• L. Onsager, Crystal statistics I. A Two-Dimensional Model With an Order-Disorder Transition, Phys. Rev., 65 (1944) 117–149.
   Google Scholar
• R. Peierls, Ising's Model of Ferromagnetism, Proc. Camb. Phil. Soc., 32 (1936), 477–481.
   Google Scholar
• D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, 1969.
   Google Scholar
• Y. G. Sinai, Theory of Phase Transitions: Rigorous Results, Pergamon Press, 1982.
   Google Scholar
• H. E. Stanley, ed., Cooperative Phenomena near Phase Transitions (A bibliography with selected readings), M.I.T. Press, 1973.
   Google Scholar
• H. E. Stanley, ed., Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, 1985.
   Google Scholar
• C. Thompson, Mathematical Statistical Mechanics, Princeton University Press, 1972.
   Google Scholar
• G. E. Uhlenbeck and G. W. Ford, Lectures in Statistical Mechanics, AMS, 1963.
   Google Scholar
• G. H. Wannier, Statistical Physics, Wiley, 1966.
   Google Scholar
• K. G. Wilson, Problems in Physics with Many Scales of Length, Scientific American, 241 (1979) 158–179.
   Web of Science ®Google Scholar
• C. N. Yang, The Spontaneous Magnetization of a Two-Dimensional Ising Model, Phys. Rev., 85 (1952) 808–816.
   Web of Science ®Google Scholar
• J. M. Ziman, Models of Disorder, Cambridge University Press, 1979.
   Google Scholar