Complete asymptotics for correlations of Laplace integrals in the semi-classical limit

 Access to full text

 Full (PDF)

1. [BJS] V. Bach, T. Jecko, J. Sjöstrand, Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature, Ann. H. Poincaré, 1(1) (2000), 52-100. Zbl1021.82002MR2001h:82009
2. [CC] J.T. Chayes, L. Chayes, Ornstein-Zernike behaviour for self-avoiding walks at all non-critical temperatures, Comm. Math. Phys. 105 (1986), 221-238. MR87k:82008
3. [DZ] R.L. Dobrushin, M. Zahradnik, Phase diagrams of continuous spin systems, Math. problems of stat. phys. and dynamics (R.L. Dobrushin, ed.), Reidel, 1986, 1-123. Zbl0611.58025MR88k:82015
4. [H1] B. Helffer, On Laplace integrals and transfer operators in large dimension, examples in the non-convex case, Lett. Math. Phys., 38(3) (1996), 297-312. Zbl0861.47051MR97j:81075
5. [H2] B. Helffer, Remarks on the decay of correlations and Witten's laplacians, Brascamp-Lieb inequalities and semi-classical limit, J. Funct. An. 155(2) (1998), 571-586. Zbl0921.35141MR2000g:82004
6. [H3] B. Helffer, Remarks on the decay of correlations and Witten's laplacians -II. Analysis of the dependence of the interaction, Rev. Math. Phys. 11(3) (1999), 321-336. Zbl1054.82002MR2000g:82005
7. [H4] B. Helffer, Remarks on the decay of correlations and Witten's laplacians -III. Applications to logarithmic Sobolev inequalities, Ann. IHP Proba. Stat., 35(4) (1999), 483-508. Zbl1055.82004MR2000g:82006
8. [HS] B. Helffer, J. Sjöstrand, On the correlation for Kac like models in the convex case, J. Stat. Phys., 74(1,2) (1994), 349-409. Zbl0946.35508MR95g:82022
9. [J] J. Johnsen, On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality, Integr. equ. oper. theory 36 (2000), 288-324. Zbl1023.58012MR2001m:58049
10. [K] H. Koch, Irreducible kernels and bound states in λP(Φ)2 models, Ann. Inst. H. Poincaré, 31(3) (1979), 173-234. 
11. [MZ] R. Minlos, E. Zhizhina, Asymptotics of the decay of correlations for Gibbs spin fields, Teoret. Mat. Fiz. 77(1) (1988), 3-12, translation in Theoret. and Math. Phys. 77(1) (1988), 1003-1009. MR90d:82009
12. [P] P.J. Paes-Leme, Ornstein-Zernike and analyticity properties for classical lattice spin systems, Ann. of Phys., 115 (1978), 367-387. Zbl0397.42011MR80a:81044
13. [Sc] R.S. Schor, The particle structure of v-dimensional Ising models at low temperatures, Comm. Math. Phys. 59 (1978), 213-233 MR58 #4122
14. [Si] B. Simon, The statistical mechanics of lattice gases, Vol. 1, Princeton ser. in physics, Princeton Univ. Press, Princeton 1993 Zbl0804.60093MR95a:82001
15. [S1] J. Sjöstrand, Correlation asymptotics and Witten Laplacians, Algebra and Analysis, 8(1) (1996), 160-191. Also St Petersburg J. Math. 8(1) (1997), 123-147. Zbl0877.35084MR97g:58168
16. [S2] J. Sjöstrand, Evolution equations in a large number of variables, Math. Nachr. 166 (1994), 17-53. Zbl0837.35061MR95h:35094
17. [S3] J. Sjöstrand, Potential wells in high dimensions I, Ann. IHP, ph. théor., 58(1) (1993), 1-41. Zbl0770.35050MR94k:81055a
18. [S4] J. Sjöstrand, Ferromagnetic integrals and maximum principles, Ann. Inst. Fourier, 44(2) (1994), 601-628. Zbl0831.35031MR95h:81015
19. [S5] J. Sjöstrand, Potential wells in high dimensions II, more about the one well case, Ann. IHP, ph. théor., 58(1) (1993), 43-53. Zbl0770.35051MR94k:81055b
20. [S6] J. Sjöstrand, Exponential convergence of the first eigenvalue divided by the dimension, for certain sequences of Schrödinger operators, Astérisque 210 (1992), 303-326. Zbl0796.35123
21. [SW] J. Sjöstrand, W.M. Wang, Supersymmetric measures and maximum principles in the complex domain. Exponential decay of Green's functions, Ann. Sci. ENS, 4ème série, 32 (1999), 347-414. Zbl0941.47033MR2000h:82050
22. [W] W.M. Wang, Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in Zd, Prepublication 99-39, Université de Paris Sud, mathématiques. 
23. [Wi] E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982), 661-692. Zbl0499.53056MR84b:58111
24. [Z1] M. Zahradnik, A short course on the Pirogov-Sinai theory, Rend. di Matematica, Ser. VII, 18, Roma (1998), 411-486. Zbl0927.60087MR2001m:82026
25. [Z2] M. Zahradnik, Contour methods and Pirogov Sinai theory for continuous spin lattice models, Preprint, 1999. 

1. J. Nourrigat, Exponential of a hamiltonian in large subsets of a lattice and applications