On the critical properties of the Edwards and the self-avoiding walk model of polymer chains

作者: A. Bovier , G. Felder , J. Fröhlich

DOI: 10.1016/0550-3213(84)90355-9

关键词:

摘要: Abstract We study the two- and three-dimensional, superrenormalizable Edwards model self-avoiding walk of polymers. Using a Schwinger-Dyson equation upper lower bounds on correlations in terms “skeleton diagrams” [6] we establish existence non-trivial continuum limit model. also prove that perturbation theory is asymptotic for these models. A fairly detailed analysis approach to critical point presented. In particular, show η d ⩾4, discuss rigorous consequences conjecture non-negative: among other implications, derive trivial γ =1, ⩾5 dimensions, corrections mean-field scaling laws are at most logarithmic four dimensions.

参考文章(14)
Alan D. Sokal, David C. Brydges, J�rg Fr�hlich, A new proof of the existence and nontriviality of the continuum ϕ{ 2 / 4 } and ϕ{ 3 / 4 } quantum field theories Communications in Mathematical Physics. ,vol. 91, pp. 141- 186 ,(1983) , 10.1007/BF01211157
Barry Simon, Correlation inequalities and the decay of correlations in ferromagnets Communications in Mathematical Physics. ,vol. 77, pp. 111- 126 ,(1980) , 10.1007/BF01982711
Harry Kesten, On the Number of Self‐Avoiding Walks Journal of Mathematical Physics. ,vol. 4, pp. 960- 969 ,(1963) , 10.1063/1.1704022
Claude Itzykson, Jean Bernard Zuber, Quantum Field Theory ,(1980)
P. G. de Gennes, Scaling Concepts in Polymer Physics ,(1979)
C.Aragão de Carvalho, S. Caracciolo, J. Fröhlich, Polymers and g|φ|4 theory in four dimensions Nuclear Physics B. ,vol. 215, pp. 209- 248 ,(1983) , 10.1016/0550-3213(83)90213-4
David Brydges, Jürg Fröhlich, Thomas Spencer, The random-walk representation of classical spin systems and correlation inequalities Communications in Mathematical Physics. ,vol. 83, pp. 123- 150 ,(1982) , 10.1007/BF01947075
J. Westwater, On Edwards' model for long polymer chains Communications in Mathematical Physics. ,vol. 72, pp. 131- 174 ,(1980) , 10.1007/3-540-11192-1_71