Stochastic geometry of classical and quantum ising models

Lecture Notes in Mathematics

Volumn 1970, Issue , 2009, Pages 87-127

  Ioffe, Dmitry ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350120595     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-92796-9_2     Document Type: Article

References (20)

1. Aizenman, M.: Geometric analysis of .4 fields and Ising models. I, II. Comm. Math. Phys. 86, 1, 1-48 (1982).
2. Aizenman, M., Ferńandez, R.: On the critical behavior of the magnetization in high-dimensional Ising models. J. Stat. Phys., 44, 3/4, 393-454 (1986).
3. Aizenman, M., Klein, A., Newman, C.M.: Percolation methods for disordered quantum Ising models, Mathematics, Physics, Biology..., R. Kotecḱy, ed., 1-24, World Scientific, Singapore (1993).
4. Aizenman, M., Nachtergaele, B.: Geometric aspects of quantum spin states. Comm. Math. Phys., 164, 1, 17-63 (1994).
5. Björnberg, J.E., Grimmett, G: The phase transition of the quantum Ising model is sharp. http://xxx.lanl.gov/pdf/0901.0328
6. Bollob́as, B.: Random Graphs, London: Academic Press (1985).
7. Bollob́as, B., Grimmett, G., Janson, S.: The random cluster model on the complete graph. Prob. Theory Rel. Fields 104, 3, 283-317 (1996). (Pubitemid 126344731)
8. Campanino, M., Klein, A., Perez, J.F.: Localization in the ground state of the Ising model with a random transverse field. Comm. Math. Phys. 135, 3, 499-515 (1991).
9. Chayes, L., Crawford, N, Io.e, D, Levit, A.: the phase diagram of the quantum Curie-Weiss model, J. stat. phys. 133, 1, 131-149 (2008).
10. Crawford, N., Io.e, D.: Random current representation for transverse field Ising models, http://xxx.lanl.gov/pdf/0812.4834
11. Dorlas, T.V.: Probabilistic derivation of a noncommutative version of Varadhan's theorem. Preprint DIAS-STP-02-5 (2002).
12. Duneau, M., Iagolnitzer, D., Souillard, B.: Strong cluster properties for classical systems with finite range interaction. Comm. Math. Phys. 35, 307-320 (1974).
13. Edwards, R.G., Sokal, A.D.: Generalization of the Fortuin-Kasteleyn- Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D, 38, 2009-2012 (1988).
14. Grimmett, G.: Space-time percolation, Preprint (2007).
15. Io.e, D., Levit, A.: Long range order and giant components of quantum random graphs. Mark. Proc. and Rel. Fields 13, 3, 469-492. (2007)
16. Janson, S.: On a random graph related to quantum theory. Combin. Probab. Comput. 16, 757-766 (2007).
17. Fannes, M., Spohn, H., Verbeure, A.: Equilibrium states for mean field models. J. Math. Phys., 21, 2, 355-358 (1980).
18. Nachtergaele, B.: Quasi-state decompositions for quantum spin systems. Probability theory and mathematical statistics (Vilnius, 1993), 565-590, TEV, Vilnius (1994).
19. Reed, M., Simon, B.: Methods of modern mathematical physics. I. Functional analysis. Second edition. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York (1980).
20. Ueltschi, D.: Geometric and probabilistic aspects of boson lattice models. In and out of equilibrium: Physics with a probability .avor, Progr. Probab. 51, 363-391, Birkhäuser (2002).