Abstract
The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of nonformal invariance and universality are established numerically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
T. W. Anderson and D. A. Darling, Asymptotic theory of certain ``goodness of fit'' criteria based on stochastic processes, Ann. Math. Statist. 23:193–212 (1952).
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, 1982).
John L. Cardy, Effect of boundary conditions on the operator content of two-dimen-sional conformably invariant theories, Nucl. Phys. B 275:200–218 (1986).
John L. Cardy, Critical percolation in finite geometries, J. Phys. A 25:L201 (1992).
John L. Cardy, Conformal invariance and statistical mechanics, in Champs, Cordes et Pheénomeènes Critiques, E. Breézin and J. Zinn-Justin, eds. (Les Couches, Session XLIX).
E. Charpentier and K. Gawedzki, Wess-Zumino-Witten conformal field theory for simply laced groups at level one, Ann. Phys. 213:233–294 (1992).
R. Chatterjee and A. Zamolodchikov, Local magnetization in critical Ising model with boundary magnetic field, Mod. Phys. Lett. A 9:2227–2234 (1992).
R. B. D'Agostino and M. A. Stephens, Goodness-of-Fit Techniques (Marcel Dekker, 1986).
J. Kertesz, D. Stauffer, and A. Coniglio, Clusters for random and intersecting per-colation in Percolation structures and processes, Ann. of the Israel Physical Society 5:122–146 (1983).
Harry Kesten, Percolation Theory for Mathematicians (Birkä user, 1982).
Robert P. Langlands, An essay on the dynamics and statistics of critical field theories, in Société mathématique du Canada 1945-1995, tome 3: Articles sollicités (Sociéte Mathématique du Canada, 1996)
R. P. Langlands, Ph. Pouliot, and Y. Saint-Aubin, Conformal invariance in two-dimensional percolation, Bull. AMS 30:1–61 (1994).
R. P. Langlands, C. Pichet, Ph. Pouliot, and Y. Saint-Aubin, On the universality of crossing probabilities in two-dimensional percolation, J. Stat. Phys. 67:553–574 (1992).
Barry M. McCoy and Tai Tsun Wu, The Two-Dimensional Ising Model (Harvard University Press, 1973).
Christian Mercat, Holomorphie discrète et modèle d'Ising, Thèse, Université Strasbourg I—Louis Pasteur (1998).
Bernard Nienhuis, Coulomb gas formulation of two-dimensional phase transitions, in Phase Transitions and Critical Phenomena, Vol. 11, Cyril Domb, ed. (Academic Press, 1987), pp. 1–53.
E. S. Pearson and M. A. Stephens, The goodness-of-fit tests based on W 2n and U 2N , Biometrika 49:397–402 (1962).
Graeme Segal, Two-dimensional conformal field theories and modular functions, in IXth International Congress on Mathematical Physics, Barry Simon et al., eds. (Adam Hilger, 1989).
Graeme Segal, Geometric aspects of quantum field theory, in Proceedings of the International Congress of Mathematicians, Kyoto 1990 (Springer Verlag, 1991).
B. W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman & Hall, 1986).
S. Tezuka and P. L'Écuyer, Efficient and portable combined Tausworthe random number generators, ACM Trans. Model. Comput. Simul. 1:99–112 (1991).
S. S. Wilks, Mathematical Statistics (Princeton University Press, 1943).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Langlands, R.P., Lewis, MA. & Saint-Aubin, Y. Universality and Conformal Invariance for the Ising Model in Domains with Boundary. Journal of Statistical Physics 98, 131–244 (2000). https://doi.org/10.1023/A:1018674822185
Issue Date:
DOI: https://doi.org/10.1023/A:1018674822185