- 1.F. Barahona. On the computational complexity of ising spin glass models. J. Phys. A: Math. Gen., 15:3241- 3253, 1982.Google Scholar
- 2.R. J. Baxter. Ezactly Solved Models in Statistical Mechanics. Academic Press, 1982.Google Scholar
- 3.N. L. Biggs. Interaction Models. Cambridge University Press, 1977.Google Scholar
- 4.S.' G. Brush. History of the lenz-ising model. Rev. Mod. Phys., 39, 1967.Google Scholar
- 5.W. Camp. Ising transfer matrix and a d-dimensional fermion model. Phys. Rev. BS, 9, 1973.Google Scholar
- 6.W. Camp and M. E. Fisher. Decay of order in classical many body systems: Introduction and fromal theory. Phys. Rev. B6, 3, 1972.Google Scholar
- 7.R. Feynman. Lectures on Statistical Mechanics. Addison-Wesley, 1972.Google Scholar
- 8.M. Fisher. On the dimer solution of the planar Ising model. J. Math. Phys., 7, 1966.Google Scholar
- 9.M. E. Fisher. Simple ising models still thrive. Physica, 106, 1981.Google Scholar
- 10.H. O. Georgii. Gibbs Measures and Phase Transitions. de Gruyter, 1988.Google Scholar
- 11.S. Goodman and S. Hedetniemi. Eulerian walks in graphs. SIAM J. Computing, 2, 1973.Google Scholar
- 12.F. O. Hadlock. Finding a maximum cut of a planar graph in polynomial time. SiAM J. Computing, 4, 1975.Google Scholar
- 13.F. Harary. Feynman's simplification of the kac-ward treatment of the two-dimensional ising problem.Google Scholar
- 14.F. Harary, editor. Graph Theory and Theoretical Physiscs. Academic Press, 1967.Google Scholar
- 15.F. Harary. A graphical exposition of the ising problem. J. Australian Mathematical Society, 1971.Google ScholarCross Ref
- 16.C. A. Hurst. Applicability of the pfaffian method to combinatorial problems on a lattice. Journal of Mathematical Physics, 3(1):90-100, 1964.Google ScholarCross Ref
- 17.C. A. Hurst. Relation between the onsager and pfaffian methods for solving the ising problem, i. the rectangular lattice. Journal of Mathematical Physics, 6(1):11-18, 1965.Google ScholarCross Ref
- 18.E. Ising. Beitrag zur theorie des ferromagnetismus. Z. Physics, 31, 1925.Google Scholar
- 19.F. Jaeger, D. L. Vertigan, and D. j. A. Welsh. On the computational complexity of the jones and tutte polynomials. Math. Proc. Camb. Phil. Soc., 108, 1990.Google Scholar
- 20.M. Jerrum. Two-dimensional monomer-dimer systems are computationally intractable, j. Star. Phys., 48(1), 1987.Google Scholar
- 21.M. R. Jerrum and S. A. Polynomial-time approximation algorithms for the ising model. Proc. 17th ICALP, EATCS, 1990. Google ScholarDigital Library
- 22.M. Kac. Enigmas of Chance. Harper and Row, 1985.Google Scholar
- 23.M. Kac and J. C. Ward. A combinatorial solution of the two dimensional ising model. Phys. Rev., 88, 1952.Google Scholar
- 24.P. W. Kasteleyn. The statistics of dimers on a lattice. i. the number of dimers arrangements of a quadratic lattice. Physica, 27, 1961.Google Scholar
- 25.P. W. Kasteleyn. Graph theory and crystal physics. Graph Theory and Theoretical Physics (F. Harary ed.), 1967.Google Scholar
- 26.H. A. Kramers and Wannier. Statistics of the twodimensional ferromagnet, i and ii. Phys. Rev., 60, 1941.Google Scholar
- 27.L. Lovasz and M. D. Plummet. Matching Theory. North-Holland, 1986. Google ScholarDigital Library
- 28.B. M. McCoy and T. T. Wu. The Two-Dimensional Ising Model Harvard University Press, 1973.Google Scholar
- 29.E. W. Montroll. Lectures on the ising model of phase transitions. Statistical Physics, Phase Transitions and Superfluidity, Brandais University Summer Institute in Theoretical Physics, 2, 1968.Google Scholar
- 30.G. F. Newell and E. W. Montroll. On the theory of the ising model of ferromagnetism. Reviews of Modern Physics, 25(2):353-389, 1953.Google ScholarCross Ref
- 31.L. Onsager. Crystal statistics i. a two'dimensional model with an order-disorder transition. Phys. Rev., 65, 1944.Google Scholar
- 32.G. I. Orlova and Y. G. Dorfman. Finding the maximum cut in a graph. Engr. Cybernetics, 10, 1972.Google Scholar
- 33.R. Peierls. Ising's model of ferromagnetism. Proc. Camb. Phil. Soc., 32, 1936.Google Scholar
- 34.S. Sherman. Combinatorial aspects of the ising model of ferromagnetism, i. a conjecture of feynman on paths and graphs. Journal of Mathematical Physics, 1(3):202- 217, 1960.Google ScholarCross Ref
- 35.H. N. V. Temperley. Two-dimensional ising models. Phase transitions and critical phenomena (Domb, C. and Green, M. $. (ed)), 1, 1974.Google Scholar
- 36.D. J. A. Welsh. The computational complexity of some classical problems from statistical physics. Disorder in physical systems, pages 307-321, 1990.Google Scholar
- 37.D. J. A. Welsh. Complexity: Knots, colouring and counting. Cambridge University Press, 1993. Google ScholarDigital Library
Index Terms
- Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces (extended abstract)
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