Editing Ising model
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<ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref> | <ref>[http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown]</ref> | ||
<ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref> | <ref>[http://dx.doi.org/10.1145/335305.335316 Sorin Istrail "Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces", Proceedings of the thirty-second annual ACM symposium on Theory of computing pp. 87-96 (2000)]</ref> | ||
In three dimensions, the | In three dimensions, the critical exponents are not known exactly. However, [[Monte Carlo | Monte Carlo simulations]] and [[Renormalisation group]] analysis provide accurate estimates: | ||
:<math> | :<math> | ||
\nu=0. | \nu=0.6298 (5) | ||
</math> | </math><ref name="Hasenbusch">[http://dx.doi.org/10.1103/PhysRevB.59.11471 M. Hasenbusch, K. Pinn and S. Vinti "Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions", Physical Review B '''59''' pp. 11471-11483 (1999)]</ref> | ||
:<math> | :<math> | ||
\alpha=0. | \alpha=0.108(5) | ||
</math> | </math> <ref name="Kolesik"> [http://dx.doi.org/10.1016/0378-4371(94)00302-A Miroslav Kolesik and Masuo Suzuki "Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method", Physica A: Statistical and Theoretical Physics '''215''' pp. 138-151 (1995)]</ref> | ||
:<math> | :<math> | ||
\beta= 0. | \beta= 0.3269(6) | ||
</math> | </math> <ref name="Talapov">[http://dx.doi.org/10.1088/0305-4470/29/17/042 A. L. Talapov and H. W. J Blöte "The magnetization of the 3D Ising model", Journal of Physics A: Mathematical and General '''29''' pp. 5727-5733 (1996)]</ref> | ||
:<math> | :<math> | ||
\gamma=1. | \gamma=1.237(4) | ||
</math> | </math><ref name="Kolesik"> </ref> | ||
:<math> | :<math> | ||
\delta=4. | \delta=4.77(5) | ||
</math> | </math><ref name="Kolesik"> </ref> | ||
:<math> | :<math> | ||
\eta =0. | \eta =0.0366(8) | ||
</math> | </math><ref name="Hasenbusch"> </ref> | ||
with a critical temperature of <math>k_BT_c = 4.51152786~S </math><ref | with a critical temperature of <math>k_BT_c = 4.51152786~S </math><ref name="Talapov"> </ref>. | ||
==ANNNI model== | ==ANNNI model== | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
==External links== | ==External links== | ||
*[http://dx.doi.org/10.4249/scholarpedia.10313 Barry McCoy "Ising model: exact results", Scholarpedia, 5(7):10313 (2010)] | *[http://dx.doi.org/10.4249/scholarpedia.10313 Barry McCoy "Ising model: exact results", Scholarpedia, 5(7):10313 (2010)] | ||
[[Category: Models]] | [[Category: Models]] |