Geodesic
An accelerated exhaustive enumeration algorithm in the Ising model
Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 2, pp. 235-244 
M. A. Padalko; P. D. Andriushchenko; K. S. Soldatov; K. V. Nefedev. An accelerated exhaustive enumeration algorithm in the Ising model. Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 2, pp. 235-244. http://geodesic.mathdoc.fr/item/DVMG_2019_19_2_a7/
@article{DVMG_2019_19_2_a7,
     author = {M. A. Padalko and P. D. Andriushchenko and K. S. Soldatov and K. V. Nefedev},
     title = {An accelerated exhaustive enumeration algorithm in the {Ising} model},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {235--244},
     year = {2019},
     volume = {19},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2019_19_2_a7/}
}
TY  - JOUR
AU  - M. A. Padalko
AU  - P. D. Andriushchenko
AU  - K. S. Soldatov
AU  - K. V. Nefedev
TI  - An accelerated exhaustive enumeration algorithm in the Ising model
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2019
SP  - 235
EP  - 244
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DVMG_2019_19_2_a7/
LA  - ru
ID  - DVMG_2019_19_2_a7
ER  - 
%0 Journal Article
%A M. A. Padalko
%A P. D. Andriushchenko
%A K. S. Soldatov
%A K. V. Nefedev
%T An accelerated exhaustive enumeration algorithm in the Ising model
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2019
%P 235-244
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/DVMG_2019_19_2_a7/
%G ru
%F DVMG_2019_19_2_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

An accelerated algorithm for the precise calculation of the lattice Ising model is presented. The algorithm makes it possible to calculate two-dimensional 8$\times$8 lattices for periodic boundary conditions on ordinary personal computers. In turn, the exact solution obtained by the proposed method makes it possible to check the effectiveness of various probabilistic approaches, in particular the Monte Carlo methods. The algorithm is applicable to various types of lattices.

[1] J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities, Oxford University Press, London, 1932 | Zbl

[2] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, V 10 t., v. 5, (V 2 ch. Ch.1) Statisticheskaya fizika, Fizmatlit, M., 2013

[3] R. D. Bakster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985

[4] N. A. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. H. Teller, “Equation of state calculation by fast computing machines”, J. Chem. Phys., 21:6 (1953), 1087–1092 | DOI

[5] R. H. Swendsen, J. S. Wang, M. N. Rosenbluth, A. H. Teller, E. H. Teller, “Nonuniversal critical dynamics in Monte-Carlo simulations”, Phys. Rev. Lett., 58:2 (1987), 86–88 | DOI | MR

[6] U. Wolff, “Collective Monte-Carlo Updating fir Spin Systems”, Phys. Rev. Lett., 2:4 (1989), 361–364 | DOI

[7] F. Wang, D. P. Landau, “Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States.”, Phys. Rev. Lett., 86:10 (2001), 2050–2053 | DOI

[8] M. E .J. Newman, G. T. Barkema, Monte Carlo Methods in Statistical Physics, Claredon Press, Oxford, 2001 | MR

[9] D. P. Landau, K. Binder, A guide to Monte Carlo simulations in statistical physics, 4th ed., Cambridge University Press, Cambridge, 2015 | MR

[10] L. Yu. Barash, M. A. Fadeeva, L. N. Shchur, “Control of accuracy in the Wang-Landau algorithm”, Phys. Rev. Lett., E 96, 043307 (2017), 2050–2053 | MR