-
5
-
-
0003975020
-
-
in edited by A. P. Young World Scientific, Singapore
-
J.-P. Bouchaud, L. F. Cugliandolo, J. Kurchan, and M. Mézard, in Spin Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore, 1998).
-
(1998)
Spin Glasses and Random Fields
-
-
Bouchaud, J.-P.1
Cugliandolo, L.F.2
Kurchan, J.3
Mézard, M.4
-
10
-
-
0037132301
-
-
10.1103/PhysRevLett.89.217202
-
M. A. Moore and B. Drossel, Phys. Rev. Lett. 89, 217202 (2002). 10.1103/PhysRevLett.89.217202
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 217202
-
-
Moore, M.A.1
Drossel, B.2
-
14
-
-
51149090376
-
-
10.1103/PhysRevLett.101.107203
-
L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, Phys. Rev. Lett. 101, 107203 (2008). 10.1103/PhysRevLett.101.107203
-
(2008)
Phys. Rev. Lett.
, vol.101
, pp. 107203
-
-
Leuzzi, L.1
Parisi, G.2
Ricci-Tersenghi, F.3
Ruiz-Lorenzo, J.J.4
-
15
-
-
72849121431
-
-
10.1103/PhysRevLett.103.267201
-
L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, Phys. Rev. Lett. 103, 267201 (2009). 10.1103/PhysRevLett.103.267201
-
(2009)
Phys. Rev. Lett.
, vol.103
, pp. 267201
-
-
Leuzzi, L.1
Parisi, G.2
Ricci-Tersenghi, F.3
Ruiz-Lorenzo, J.J.4
-
19
-
-
33645532865
-
-
10.1103/PhysRevLett.96.137202
-
M. A. Moore, Phys. Rev. Lett. 96, 137202 (2006). 10.1103/PhysRevLett.96. 137202
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 137202
-
-
Moore, M.A.1
-
20
-
-
77954822488
-
-
The model studied in Ref. has R=0.88;
-
The model studied in Ref. has R = 0.88
-
-
-
-
21
-
-
77954833447
-
-
J. Yeo (private communication).
-
J. Yeo, (private communication).
-
-
-
-
22
-
-
65549088216
-
-
10.1088/0022-3719/18/15/013
-
L. Viana and A. J. Bray, J. Phys. C 18, 3037 (1985). 10.1088/0022-3719/ 18/15/013
-
(1985)
J. Phys. C
, vol.18
, pp. 3037
-
-
Viana, L.1
Bray, A.J.2
-
25
-
-
17144462455
-
-
10.1103/PhysRevB.62.14237
-
H. G. Ballesteros, A. Cruz, L. A. Fernandez, V. Martin-Mayor, J. Pech, J. J. Ruiz-Lorenzo, A. Tarancon, P. Tellez, C. L. Ullod, and C. Ungil, Phys. Rev. B 62, 14237 (2000). 10.1103/PhysRevB.62.14237
-
(2000)
Phys. Rev. B
, vol.62
, pp. 14237
-
-
Ballesteros, H.G.1
Cruz, A.2
Fernandez, L.A.3
Martin-Mayor, V.4
Pech, J.5
Ruiz-Lorenzo, J.J.6
Tarancon, A.7
Tellez, P.8
Ullod, C.L.9
Ungil, C.10
-
27
-
-
77954824871
-
-
For a discussion of how finite-size scaling is modified in the region of mean-field exponents, see, for example, Refs.
-
For a discussion of how finite-size scaling is modified in the region of mean-field exponents, see, for example, Refs.
-
-
-
-
28
-
-
33344476954
-
-
10.1103/PhysRevB.71.174438
-
J. L. Jones and A. P. Young, Phys. Rev. B 71, 174438 (2005). 10.1103/PhysRevB.71.174438
-
(2005)
Phys. Rev. B
, vol.71
, pp. 174438
-
-
Jones, J.L.1
Young, A.P.2
-
30
-
-
33744620852
-
-
10.1103/PhysRevB.38.386
-
D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 386 (1988). 10.1103/PhysRevB.38.386
-
(1988)
Phys. Rev. B
, vol.38
, pp. 386
-
-
Fisher, D.S.1
Huse, D.A.2
-
31
-
-
77954822632
-
-
One can alternatively reexpress the FSS results in Eqs. in the following way. A thermodynamic quantity X has the finite-size scaling form X = L yx x [ L yT (T- tc ) , L yH h ], where yT =1/ν and yH = (d+2-η ) /2 are the thermal and magnetic exponents. The connection between LR and SR exponents is obtained by writing this in terms of the total number of spins N and equating the exponents, i.e., yT,LR = yT,SR / deff , yH,LR = yH,SR / deff , yX,LR = yX,SR / deff. In the same way, the analogous result for the correction to scaling exponent ω is ωLR = ωSR / deff. The relation involving yX does not apply for the correlation length since it refers to a linear dimension, rather than a volume, and so there is no factor of deff, see Eq. .
-
One can alternatively reexpress the FSS results in Eqs. in the following way. A thermodynamic quantity X has the finite-size scaling form X = L y X X [L y T (T - t c), L y H h], where y T = 1 / ν and y H = (d + 2 - η) / 2 are the thermal and magnetic exponents. The connection between LR and SR exponents is obtained by writing this in terms of the total number of spins N and equating the exponents, i.e., y T, LR = y T, SR / d eff, y H, LR = y H, SR / d eff, y X, LR = y X, SR / d eff. In the same way, the analogous result for the correction to scaling exponent ω is ω LR = ω SR / d eff. The relation involving y X does not apply for the correlation length since it refers to a linear dimension, rather than a volume, and so there is no factor of d eff, see Eq.
-
-
-
-
33
-
-
1542641001
-
-
10.1016/0370-2693(96)00984-7
-
H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, and A. Muñoz Sudupe, Phys. Lett. B 387, 125 (1996). 10.1016/0370-2693(96)00984-7
-
(1996)
Phys. Lett. B
, vol.387
, pp. 125
-
-
Ballesteros, H.G.1
Fernández, L.A.2
Martín-Mayor, V.3
Muñoz Sudupe, A.4
-
37
-
-
0001740438
-
-
10.1103/PhysRevB.31.1498
-
K. Binder, M. Nauenberg, V. Privman, and A. P. Young, Phys. Rev. B 31, 1498 (1985). 10.1103/PhysRevB.31.1498
-
(1985)
Phys. Rev. B
, vol.31
, pp. 1498
-
-
Binder, K.1
Nauenberg, M.2
Privman, V.3
Young, A.P.4
-
39
-
-
77954823695
-
-
This expression vanishes for σ= σc =2/3 as expected. Furthermore, using the connection between σ and the effective dimension of a short-range model in Eq. , we have ω= ωSR /d with ωSR = (d-6 ) /2, as expected at the trivial Gaussian fixed point in a cubic field theory (Ref.).
-
This expression vanishes for σ = σ c = 2 / 3 as expected. Furthermore, using the connection between σ and the effective dimension of a short-range model in Eq., we have ω = ω SR / d with ω SR = (d - 6) / 2, as expected at the trivial Gaussian fixed point in a cubic field theory (Ref.).
-
-
-
-
40
-
-
0019931021
-
-
10.1051/jphys:0198200430101500
-
E. Brézin, J. Phys. France 43, 15-22 (1982). 10.1051/jphys: 0198200430101500
-
(1982)
J. Phys. France
, vol.43
, pp. 15-22
-
-
Brézin, E.1
|