@article{AIHPA_1988__49_1_87_0, author = {Bleher, P. M. and Major, P.}, title = {The large-scale limit of {Dyson's} hierarchical vector-valued model at low temperatures. {The} non-gaussian case. {Part} {II} : description of the large-scale limit}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {87--143}, publisher = {Gauthier-Villars}, volume = {49}, number = {1}, year = {1988}, mrnumber = {974869}, zbl = {0669.60096}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1988__49_1_87_0/} }
TY - JOUR AU - Bleher, P. M. AU - Major, P. TI - The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit JO - Annales de l'I.H.P. Physique théorique PY - 1988 SP - 87 EP - 143 VL - 49 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1988__49_1_87_0/ LA - en ID - AIHPA_1988__49_1_87_0 ER -
%0 Journal Article %A Bleher, P. M. %A Major, P. %T The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit %J Annales de l'I.H.P. Physique théorique %D 1988 %P 87-143 %V 49 %N 1 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1988__49_1_87_0/ %G en %F AIHPA_1988__49_1_87_0
Bleher, P. M.; Major, P. The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit. Annales de l'I.H.P. Physique théorique, Tome 49 (1988) no. 1, pp. 87-143. http://www.numdam.org/item/AIHPA_1988__49_1_87_0/
[1] Discontinuity of the magnetization in one-dimensional 1/|x - y|2 Ising and Potts models. J. Stat. Phys., t. 50, 1988, p. 1-40. | MR | Zbl
, , , ,[2] Discontinuity of the percolation density in one-dimensional 1/|x - y|2 percolation models. Commun. Math. Phys., t. 107, 1986, p. 611-647. | MR | Zbl
, ,[3] Convergence of probability measures. Wiley, 1968. | MR | Zbl
,[4] Construction of non-Gaussian self-similar random fields with hierarchical structure. Commun. Math. Phys., t. 87, 1982, p. 226-240. | MR | Zbl
,[5] Renormalization of Dyson's hierarchical vector-valued Φ4-model at low temperatures. Commun. Math. Phys., t. 95, 1984, p. 487-532. | MR | Zbl
, ,[6] Critical phenomena and universal exponents in statistical physics. On Dyson's hierarchical model. The Annals of Probability, t. 15, 1987, p. 431-477. | MR | Zbl
, ,[7] Limit theorems in statistical physics; On Dyson's hierarchical model. In the conference volume of the first world conference of the Bernoulli Society. | Zbl
, ,[8] Investigation of the critical point in models of the type of Dyson's hierarchical model. Commun. Math. Phys., t. 33, 1973, p. 23-42.
, ,[9] Critical indices for Dyson's asymptotically hierarchical models. Commun. Math. Phys., t. 45, 1975, p. 247-278.
, ,[10] Definition of random variables by conditional distributions. Teor. Veroyatn. Primen, t. 15, 1970, p. 469-497. | MR | Zbl
,[11] Gaussian and their subordinated self-similar fields. Annals of Probability, t. 7, 1979, p. 1-28. | MR | Zbl
,[12] Existence of phase transition in a one-dimensional Ising ferromagnet. Commun. Math. Phys., t. 42, 1969, p. 31-40. | MR
,[13] An Ising ferromagnet with discontinuous long range order. Commun. Math. Phys., t. 21, 1971, p. 269-283. | MR
,[14] Infrared bounds, phase transitions and continuous symmetry breaking. Commun. Math. Phys., t. 50, 1976, p. 79-85. | MR
, , ,[15] The Kosterlitz-Thouless transition in two-dimensional Abelian spin system and the Coulomb gas. Commun. Math. Phys., t. 81, 1981, p. 527-602. | MR
, ,[16] Multiple Wiener-Itô integrals with applications to limit theorems. Lecture Notes in Mathematics, 849, Springer, 1981. | MR | Zbl
,[17] One-dimensional 1/|j - i|s percolation models; The existence of a transition for s ≤ 2. Commun. Math. Phys., t. 104, 1986, p. 547-571. | MR | Zbl
, ,[18] Interaction of Goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields. Phys. Lett., t. 59 B, n° 1, 1975, p. 79-81.
,[19] Gibbs states on countable sets. Cambridge Tracts, 68 Cambridge University Press, London, 1974. | MR | Zbl
,[20] Theory of phase transitions. Rigorous results. Pergamon, New York, 1982. | MR | Zbl
,[21] The renormalization group and the ∈-expansion. Phys. Rept., t. 12 C, 2, 1974, p. 75-199.
, ,[22] A different perspective of the Kosterlitz-Thouless phase transition, to appear in Phys. Rev. Lett. | MR
, ,[23] Critical behaviour, scaling and universality in some two dimensional spin models, working paper, 1987.
, , , ,