Complete asymptotics for correlations of Laplace integrals in the semi-classical limit (2000)


Sjöstrand, Johannes
Mémoires de la Société Mathématique de France, Tome 83 (2000) 114 p doi : 10.24033/msmf.396
URL stable : http://www.numdam.org/item?id=MSMF_2000_2_83__1_0

Bibliographie

[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. MR 2001h:82009 | Zbl 01533502

[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. MR 87k:82008

[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. MR 88k:82015 | Zbl 0611.58025

[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. MR 97j:81075 | Zbl 0861.47051

[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. MR 2000g:82004 | Zbl 0921.35141

[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. MR 2000g:82005 | Zbl 01540544

[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. Numdam | MR 2000g:82006 | Zbl 01340477

[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. MR 95g:82022 | Zbl 0946.35508

[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. MR 2001m:58049 | Zbl 01454719

[K] H. Koch, Irreducible kernels and bound states in λP(Φ)2 models, Ann. Inst. H. Poincaré, 31(3) (1979), 173-234. Numdam |

[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. MR 90d:82009

[P] P.J. Paes-Leme, Ornstein-Zernike and analyticity properties for classical lattice spin systems, Ann. of Phys., 115 (1978), 367-387. MR 80a:81044 | Zbl 0397.42011

[Sc] R.S. Schor, The particle structure of v-dimensional Ising models at low temperatures, Comm. Math. Phys. 59 (1978), 213-233 MR 58 #4122

[Si] B. Simon, The statistical mechanics of lattice gases, Vol. 1, Princeton ser. in physics, Princeton Univ. Press, Princeton 1993 MR 95a:82001 | Zbl 0804.60093

[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. MR 97g:58168 | Zbl 0877.35084

[S2] J. Sjöstrand, Evolution equations in a large number of variables, Math. Nachr. 166 (1994), 17-53. MR 95h:35094 | Zbl 0837.35061

[S3] J. Sjöstrand, Potential wells in high dimensions I, Ann. IHP, ph. théor., 58(1) (1993), 1-41. Numdam | MR 94k:81055a | Zbl 0770.35050

[S4] J. Sjöstrand, Ferromagnetic integrals and maximum principles, Ann. Inst. Fourier, 44(2) (1994), 601-628. Numdam | MR 95h:81015 | Zbl 0831.35031

[S5] J. Sjöstrand, Potential wells in high dimensions II, more about the one well case, Ann. IHP, ph. théor., 58(1) (1993), 43-53. Numdam | MR 94k:81055b | Zbl 0770.35051

[S6] J. Sjöstrand, Exponential convergence of the first eigenvalue divided by the dimension, for certain sequences of Schrödinger operators, Astérisque 210 (1992), 303-326. Zbl 0796.35123

[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. Numdam | MR 2000h:82050 | Zbl 0941.47033

[W] W.M. Wang, Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in Zd, Prepublication 99-39, Université de Paris Sud, mathématiques.

[Wi] E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982), 661-692. MR 84b:58111 | Zbl 0499.53056

[Z1] M. Zahradnik, A short course on the Pirogov-Sinai theory, Rend. di Matematica, Ser. VII, 18, Roma (1998), 411-486. MR 2001m:82026 | Zbl 0927.60087

[Z2] M. Zahradnik, Contour methods and Pirogov Sinai theory for continuous spin lattice models, Preprint, 1999.