Numerical study of the 6-Vertex model with domain wall boundary conditions

Annales de l'Institut Fourier

Volumn 55, Issue 6, 2005, Pages

  Allison, David ^a   Reshetikhin, Nicolai ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

6 vertex; Markov chain; Monte Carlo; Random sampling

Indexed keywords

EID: 34250864374     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.2144     Document Type: Conference Paper

References (20)

1. H. COHN, M. LARSEN, J. PROPP, The shape of a typical boxed plane partition, New York J. Math., 4 (1998), 137-165.
2. H. COHN, N. ELKIS, J. PROPP, Local statistics of random domino tilings of the Aztec diamons, Duke Math. J., 85 (1996), 117-166.
3. R.J. BAXTER, Exactly Solved Models in Statistical Mechanics, Academic Press, San Diego, 1982.
4. K. ELORANTA, Diamond Ice, J. Statist. Phys., 96 (1999), no. 5-6, 1091-1109.
5. A. IZERGIN, Partition function of the 6-vertex model in a finite volume, Sov. Phys. Dokl., 32 (1987), 878-879.
6. R. KENYON, An introduction to the dimer models.math.PR/0308284.
7. V. KOREPIN, P. ZINN-JUSTIN, Thermodynamic limit of the six-vertex model with domain wall boundary conditions.cond-mat/ 0004250.
8. V.E. KOREPIN, Calculation of norms of Bethe wave functions, Comm. Math. Phys., 86 (1982), no. 3, 391-418.
9. G. KUPERBERG, Another proof of the alternating-sign matrix conjecture, Int. Math. Res. Notes, 3 (1996), 139-150.
10. E. LIEB, F. WU, Two dimensional ferroelectric models, in 'Phase transitions and critical phenomena', ed. by C. Domb, and M.S. Green, Academic Press, 1972.
11. R. KENYON, A. OKOUNKOV, S. SHEFFIELD, Dimers and amoebae.math-ph/031 1005.
12. A. OKOUNKOV, N. RESHETIKHIN, Random skew plane partitions and the Pearcey process, math.CO/0503508.
13. A. OKOUNKOV, N. RESHETIKHIN, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, J. Amer. Math. Soc., 16 (2003), no. 3, 581-603.
14. J. PROPP, D. WILSON, Coupling from the past: a user's guide, in 'Microsurveys in Discrete Probability' (Princeton, NJ, 1997), DIMACS Ser. Discrete Math. Theoret. Comp. Sci., AMS, 41, 181-192 (1998).
15. A. SINCLAIR, Algorithms for Random Generation and Counting, Birkhauser, Boston, 1993.
16. O.F. SYLJUASEN, M.B. ZVONAREV, Directed-loop Monte Carlo simulations of vertex models cond-mat/0401491.
17. A.V. RAZUMOV, Yu. STROGANOV, Combinatorial structure of the ground state of O(1) loop model math.CO/0104216.
18. Asymptotic combinatorics with applications to mathematical physics (ed. by A.M. Vershik), Lecture Notes in Math. 1815, Springer, 2003.
19. P. ZINN-JUSTIN, Six-vertex model with domain wall boundary conditions and one-matrix model, Phys. Rev. E (3), 62 (2000), no. 3, part A, 3411-3418.
20. J.-B. ZUBER, On the counting of fully packed loop configurations. Some new conjectures.math-ph/0309057.