-
7
-
-
0035798529
-
-
At present the most accurate estimates of are =0.587 58±0.000 07 (Ref.), =0.5874±0.0002 [, 0305-4470 10.1088/0305-4470/34/43/102, ()]; =0.58765±0.00020 [, Macromolecules 0024-9297 10.1021/ma0355958 37, 4658 (2004)]; =0.5876±0.0002 [, J. Phys. A 0305-4470 10.1088/1751-8113/40/26/ F05 40, F539 (2007)]; =0.5876±0.0002 [, J. Phys. A 0305-4470 10.1088/1751-8113/40/36/003 40, 10973 (2007)] (assuming 0.50θ0.53); For an extensive list of older results, see, Phys. Re 368, 549 (2002).
-
At present the most accurate estimates of are =0.587 58±0.000 07 (Ref.), =0.5874±0.0002 [T. Prellberg, J. Phys. A 0305-4470 10.1088/0305-4470/34/43/102 34, L599 (2001)]; =0.58765±0.00020 [H. -P. Hsu, W. Nadler, and P. Grassberger, Macromolecules 0024-9297 10.1021/ma0355958 37, 4658 (2004)]; =0.5876±0.0002 [A. Pelissetto and E. Vicari, J. Phys. A 0305-4470 10.1088/1751-8113/40/26/F05 40, F539 (2007)]; =0.5876±0.0002 [N. Clisby, R. Liang, and G. Slade, J. Phys. A 0305-4470 10.1088/1751-8113/40/ 36/003 40, 10973 (2007)] (assuming 0.50θ0.53); For an extensive list of older results, see A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002).
-
(2001)
J. Phys. A
, vol.34
, pp. 599
-
-
Prellberg, T.1
Hsu, H.-P.2
Nadler, W.3
Grassberger, P.4
Pelissetto, A.5
Vicari, E.6
Clisby, N.7
Liang, R.8
Slade, G.9
Pelissetto, A.10
Vicari, E.11
-
8
-
-
33748539425
-
-
0021-9606 10.1063/1.2339015, ();, J. Chem. Phys. 0021-9606 10.1063/1.2722753 126, 169901 (2007) (erratum).
-
S. Caracciolo, B. M. Mognetti, and A. Pelissetto, J. Chem. Phys. 0021-9606 10.1063/1.2339015 125, 094904 (2006); S. Caracciolo, B. M. Mognetti, and A. Pelissetto, J. Chem. Phys. 0021-9606 10.1063/1.2722753 126, 169901 (2007) (erratum).
-
(2006)
J. Chem. Phys.
, vol.125
, pp. 094904
-
-
Caracciolo, S.1
Mognetti, B.M.2
Pelissetto, A.3
Caracciolo, S.4
Mognetti, B.M.5
Pelissetto, A.6
-
11
-
-
0039623302
-
-
0022-3719 10.1088/0022-3719/5/9/009.
-
C. Domb and G. S. Joyce, J. Phys. C 0022-3719 10.1088/0022-3719/5/9/009 5, 956 (1972).
-
(1972)
J. Phys. C
, vol.5
, pp. 956
-
-
Domb, C.1
Joyce, G.S.2
-
13
-
-
0000020015
-
-
0021-9606 10.1063/1.453152.
-
R. Dickman, J. Chem. Phys. 0021-9606 10.1063/1.453152 87, 2246 (1987).
-
(1987)
J. Chem. Phys.
, vol.87
, pp. 2246
-
-
Dickman, R.1
-
17
-
-
49149093303
-
-
The residual error on K can be estimated by assuming Kest (M) =K+a/ M4. It follows Δ Kest (M) - Kest (2M) =15a/ (2M) 4, so that Kest (2M) -K=Δ/15. In the two cases we show, the expected systematic error on the value corresponding to M=128 is therefore much smaller than the statistical error.
-
The residual error on K can be estimated by assuming Kest (M) =K+a/ M4. It follows Δ Kest (M) - Kest (2M) =15a/ (2M) 4, so that Kest (2M) -K=Δ/15. In the two cases we show, the expected systematic error on the value corresponding to M=128 is therefore much smaller than the statistical error.
-
-
-
-
18
-
-
0027591234
-
-
0024-9297 10.1021/ma00063a016.
-
G. Merkle, W. Burchard, P. Lutz, K. F. Freed, and J. Gao, Macromolecules 0024-9297 10.1021/ma00063a016 26, 2736 (1993).
-
(1993)
Macromolecules
, vol.26
, pp. 2736
-
-
Merkle, G.1
Burchard, W.2
Lutz, P.3
Freed, K.F.4
Gao, J.5
-
19
-
-
49149121047
-
-
The results of Ref. are expressed in terms of a variable X such that fZ (X) =1+X+O (X2) for X→0. The variable X is related to by X=1.313 [see Eq.].
-
The results of Ref. are expressed in terms of a variable X such that fZ (X) =1+X+O (X2) for X→0. The variable X is related to by X=1.313 [see Eq.].
-
-
-
-
20
-
-
49149103946
-
-
Equation (17.52) of Ref. gives the following expression for Z: Z=1+1.314 (H1 / H2) 0.309, H1 =1+2.15+1.00 2, and H2 =1+0.51. The variable s used in Ref. is related to by =1.169 s (see Sec. 13.3.2). For →∞ it predicts Z≈1.618 1.309.
-
Equation (17.52) of Ref. gives the following expression for Z: Z=1+1.314 (H1 / H2) 0.309, H1 =1+2.15+1.00 2, and H2 =1+0.51. The variable s used in Ref. is related to by =1.169 s (see Sec. 13.3.2). For →∞ it predicts Z≈1.618 1.309.
-
-
-
-
21
-
-
0000442914
-
-
0024-9297 10.1021/ma50004a042.
-
I. Noda, N. Kato, T. Kitano, and M. Nasagawa, Macromolecules 0024-9297 10.1021/ma50004a042 14, 668 (1981).
-
(1981)
Macromolecules
, vol.14
, pp. 668
-
-
Noda, I.1
Kato, N.2
Kitano, T.3
Nasagawa, M.4
-
22
-
-
0012673883
-
-
0305-4470 10.1088/0305-4470/16/17/030.
-
T. Ohta and A. Nakanishi, J. Phys. A 0305-4470 10.1088/0305-4470/16/17/ 030 16, 4155 (1983).
-
(1983)
J. Phys. A
, vol.16
, pp. 4155
-
-
Ohta, T.1
Nakanishi, A.2
-
23
-
-
51149219988
-
-
0021-9606 10.1063/1.445744.
-
K. F. Freed, J. Chem. Phys. 0021-9606 10.1063/1.445744 79, 6357 (1983).
-
(1983)
J. Chem. Phys.
, vol.79
, pp. 6357
-
-
Freed, K.F.1
-
24
-
-
0001168249
-
-
0024-9297 10.1021/ma00137a012.
-
L. Schäfer, Macromolecules 0024-9297 10.1021/ma00137a012 17, 1357 (1984).
-
(1984)
Macromolecules
, vol.17
, pp. 1357
-
-
Schäfer, L.1
-
25
-
-
0003133090
-
-
0026-8976 10.1080/00268976900100781.
-
M. Lal, Mol. Phys. 0026-8976 10.1080/00268976900100781 17, 57 (1969).
-
(1969)
Mol. Phys.
, vol.17
, pp. 57
-
-
Lal, M.1
-
26
-
-
0000790809
-
-
0305-4470 10.1088/0305-4470/18/13/037.
-
B. MacDonald, N. Jan, D. L. Hunter, and M. O. Steinitz, J. Phys. A 0305-4470 10.1088/0305-4470/18/13/037 18, 2627 (1985).
-
(1985)
J. Phys. A
, vol.18
, pp. 2627
-
-
MacDonald, B.1
Jan, N.2
Hunter, D.L.3
Steinitz, M.O.4
-
27
-
-
5944256461
-
-
0022-4715 10.1007/BF01022990.
-
N. Madras and A. D. Sokal, J. Stat. Phys. 0022-4715 10.1007/BF01022990 50, 109 (1988).
-
(1988)
J. Stat. Phys.
, vol.50
, pp. 109
-
-
Madras, N.1
Sokal, A.D.2
-
29
-
-
0036261743
-
-
0022-4715 10.1023/A:1015447704106.
-
M. S. Causo, J. Stat. Phys. 0022-4715 10.1023/A:1015447704106 108, 247 (2002).
-
(2002)
J. Stat. Phys.
, vol.108
, pp. 247
-
-
Causo, M.S.1
-
30
-
-
0037419257
-
-
0305-4470 10.1088/0305-4470/36/13/103.
-
M. S. Causo and S. G. Whittington, J. Phys. A 0305-4470 10.1088/0305-4470/36/13/103 36, L189 (2003).
-
(2003)
J. Phys. A
, vol.36
, pp. 189
-
-
Causo, M.S.1
Whittington, S.G.2
-
34
-
-
49149108573
-
-
This is true if the determination of the number of walks going through a given lattice point takes a time of order 1. This can be obtained by using, e.g., a hash table. A practical implementation is discussed in, (Addison-Wesley, Reading, MA), Vol., see Algorithm C, and Exercise 23 in Sec. 6.4.
-
This is true if the determination of the number of walks going through a given lattice point takes a time of order 1. This can be obtained by using, e.g., a hash table. A practical implementation is discussed in D. E. Knuth, The Art of Computer Programming (Addison-Wesley, Reading, MA, 1973), Vol. 3, see Algorithm C, p. 514, and Exercise 23 in Sec. 6.4.
-
(1973)
The Art of Computer Programming
, vol.3
, pp. 514
-
-
Knuth, D.E.1
|