Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1993-05-08
Europhys.Lett.27:661-666,1994; Erratum-ibid.30:123,1995
Physics
High Energy Physics
High Energy Physics - Lattice
10 pages including 1 figure, 181159 bytes Postscript (NYU-TH-93/05/01)
Scientific paper
10.1209/0295-5075/27/9/005 10.12
Previous theories of dilute polymer solutions have failed to distinguish clearly between two very different ways of taking the long-chain limit: (I) $N \to\infty$ at fixed temperature $T$, and (II) $N \to\infty$, $T \to T_\theta$ with $x \equiv N^\phi (T-T_\theta)$ fixed. I argue that the modern two-parameter theory (continuum Edwards model) applies to case II --- not case I --- and in fact gives exactly the crossover scaling functions for $x \ge 0$ modulo two nonuniversal scale factors. A Wilson-type renormalization group clarifies the connection between crossover scaling functions and continuum field theories. [Also contains a general discussion of the connection between the Wilson and field-theoretic renormalization groups. Comments solicited.]
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