Abstract
We consider the φ4 quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m(σ) decreases continuously to zero as the bare mass parameter σ approaches a critical value σ c from above. In three dimensions the critical point σ c is in the single phase region and the physical mass vanishes there,m(σ c )=0.
A consequence of our results is that the critical exponentv governing the approach to infinite correlations is bounded below (rigorously) by its classical value, 1/2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nelson, E.: Probability theory and Euclidean field theory. In: Constructive quantum field theory (eds. G. Velo, A.S. Wightman). Berlin-Heidelberg-New York: Springer 1973
Simon, B.: TheP(φ)2 Euclidean (quantum) field theory. Princeton: Princeton University Press 1974
Griffiths, R.: J. Math. Phys.8, 478–489 (1967)
Guerra, F., Rosen, L., Simon, B.: Ann. Math.101, 111–259 (1975)
Glimm, J., Jaffe, A., Spencer, T.: In: Constructive quantum field theory (eds. G. Velo, A. S. Wightman). Berlin-Heidelberg-New York: Springer 1973
Magnen, J., Sénéor, R.: Ann. Inst. H. Poincaré24, 95–159 (1976)
Feldman, J., Osterwalder, K.: The Wightman axioms and the mass gap for weakly coupled φ 43 quantum field theories. Harvard University Preprint, 1975
Glimm, J., Jaffe, A., Spencer, T.: Commun. math. Phys.45, 203–216 (1975)
Frohlich, J., Simon, B., Spencer, T.: Phase transitions and continuous symmetry breaking. The Rockefeller University preprint, 1975
Glimm, J., Jaffe, A.: Phys. Rev. D10, 536–539 (1974)
Dyson, F.: Commun. math. Phys.21, 269–283 (1971)
McCoy, B., Wu, T.T.: The two-dimensional Ising model. Cambridge: Harvard University 1973
Lebowitz, J.L.: Commun. math. Phys.35, 87–92 (1974)
Griffiths, R., Simon, B.: Commun. math. Phys.33, 145–164 (1973)
Baker, G.: J. Math. Phys.16, 1324–1346 (1975)
Rosen, J.: Mass renormalization for the λφ4 Euclidean lattice field. Adv. Math., to appear
Osterwalder, K., Schrader, R.: Commun. math. Phys.42, 281–305 (1975)
Glimm, J., Jaffe, A.: J. Math. Phys.13, 1568–1584 (1972)
Seiler, E., Simon, B.: Nelson's symmetry and all that in the Yukawa and (φ4)3 field theories. Princeton preprint
Author information
Authors and Affiliations
Additional information
Communicated by A.S. Wightman
Supported in part by the National Science Foundation under Grant MPS74-13252
Rights and permissions
About this article
Cite this article
McBryan, O.A., Rosen, J. Existence of the critical point in φ4 field theory. Commun.Math. Phys. 51, 97–105 (1976). https://doi.org/10.1007/BF01609341
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01609341