Table 1.

Analytical and simulation results for critical exponent ν of linear chains (ρ = 1, ν_path = ν) for different solvent conditions and spatial dimensionality d. “ $\frac{\delta \nu }{\delta {\nu }_{\text{ideal}}}\equiv \frac{\nu -{\nu }_{\text{true}}}{{\nu }_{\text{true}}-{\nu }_{\text{ideal}}}\times 100$ is the relative discrepancy between the actual and the true values (in boldface) of ν over the difference between the latter and the ideal value. Currently available exact values or best estimates (in boldface) are reported as symbols in Fig. 3, where predictions of Flory theory are shown as lines.

Linear chains
d	ν	δν	$\frac{\delta \nu }{\delta {\nu }_{\text{ideal}}}$	Technique	Reference
Dilute solution in a good solvent
2	3/4 = 0.75	0	0%	Flory theory	Flory (1969)74
2	3/4 = 0.75	–	–	Exact calculation	Nienhuis (1982)44
2	0.74963±0.00008	−0.00037	−0.2%	Monte Carlo	Li, Madras & Sokal (1995)56
3	3/5 = 0.6	0.0123	14%	Flory theory	Flory (1969)74
3	0.588±0.001	0.0003	0.3%	Renormalization group	Le Guillou & Zinn-Justin (1977)40
3	0.5877±0.0006	–	–	Monte Carlo	Li, Madras & Sokal (1995)56
Dilute solution in a θ-solvent
2	2/3 = 0.667	0.0952	133%	Flory theory	Flory (1969)74
2	367/726 ≈ 0.5055	−0.0659	-92%	ε-expansion	De Gennes (1975)39
2	4/7 ≈ 0.5714	–	–	Exact calculation	Duplantier & Saleur (1987)47
2	0.57±0.02	−0.0014	-2%	Monte Carlo	Wittkop, Kreitmeier & Göritz (1996)57
3	1/2 = 0.5	0	0%	Flory theory	Flory (1969)74
3	1/2 = 0.5	–	–	ε-expansion	De Gennes (1975)39
3	0.50±0.02	0.00	0%	Monte Carlo	Wittkop, Kreitmeier & Göritz (1996)57
Melt
2	1/2 = 0.5	0	0%	Flory theory	Isaacson & Lubensky (1980)11
2	1/2 = 0.5	–	–	Conformal theory	Duplantier (1986)46
3	1/2 = 0.5	–	–	Flory theory	Isaacson & Lubensky (1980)11