Communications in Mathematical Physics

, Volume 59, Issue 2, pp 117–142 | Cite as

Existence of three phases for aP(ϕ)2 model of quantum field

  • K. Gawędzki


In the two-dimensional model of the quantum field theory with lagrangean density :(∂μϕ)2−(−ν)ϕ2λ1/2 ϕ4−λϕ6: there exist (at least) three different phases for small λ and some ν(λ).


Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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  1. 1.
    Dimock, J., Glimm, J.: Measures on Schwartz distribution space and applications toP(ϕ)2 field theories. Advan. Math.12, 58–83 (1974)Google Scholar
  2. 2.
    Fröhlich, J.: Phase transitions in two dimensional quantum field models. ZIF, University of Bielefeld. PreprintGoogle Scholar
  3. 3.
    Fröhlich, J.: Phase transitions, Goldstone bosons and topological superselection rules. Acta Phys. Austr. Supl.15, 133–269 (1976)Google Scholar
  4. 4.
    Fröhlich, J., Simon, B.: Pure states for generalP(ϕ)2 theories: construction, regularity and variational equality. Princeton PreprintGoogle Scholar
  5. 5.
    Fröhlich, J., Simon, B., Spencer, T.: Infrared bounds, phase transitions and continuous symmetry breaking. Commun. math. Phys.50, 79–95 (1976)Google Scholar
  6. 6.
    Glimm, J., Jaffe, A., Spencer, T.: Phase transitions for ϕ24 quantum fields. Commun. math. Phys.45, 203–216 (1975)Google Scholar
  7. 7.
    Glimm, J., Jaffe, A., Spencer, T.: Convergent expansion about mean field theory. I and II. Ann. Phys.101, 610–630 (1976);101, 631–669 (1976)Google Scholar
  8. 8.
    Guerra, F., Rosen, L., Simon, B.: Nelson's symmetry and the infinite behavior of the vacuum inP(ϕ)2. Commun. math. Phys.27, 10–22 (1972)Google Scholar
  9. 9.
    Guerra, F., Rosen, L., Simon, B.: TheP(ϕ)2 Euclidean quantum field theory as classical statistical mechanics. I and II. Ann. Math.101, 111–189 (1975);101, 191–259 (1975)Google Scholar
  10. 10.
    Guerra, F., Rosen, L., Simon, B.: Boundary conditions for theP(ϕ)2 Euclidean field theory. Ann. Inst. H. Poincaré25, 231–334 (1976)Google Scholar
  11. 11.
    Pirogov, S.A., Sinai, Ya.G.: Phase diagrams of the classical lattice systems. I and II. Teor. Mat. Fis.25, 358–369 (1975);26, 61–76 (1976)Google Scholar
  12. 12.
    Simon, B.: TheP(ϕ)2 Euclidean (quantum) field theory. Princeton, New Jersey: Princeton University Press 1974Google Scholar
  13. 13.
    Sinai, Ya.G.: 1977 lectures in IHES, Bures-sur-YvetteGoogle Scholar
  14. 14.
    Glimm, J., Jaffe, A.: On approach to the critical point. Ann. Inst. H. Poincaré22, 109–122 (1975)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • K. Gawędzki
    • 1
  1. 1.Department of Mathematical Methods of PhysicsWarsaw UniversityWarsawPoland

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