-
1
-
-
0004098212
-
-
D. Henderson, ed., Marcel Dekker, New York
-
R. Evans, in Fundamentals of Inhomogeneous Fluids, D. Henderson, ed., Marcel Dekker, New York, 1992.
-
(1992)
Fundamentals of Inhomogeneous Fluids
-
-
Evans, R.1
-
4
-
-
0004248705
-
-
North-Holland, Amsterdam
-
H. N. V. Temperley, J. S. Rowlinson, and G. S. Rushbrooke, Physics of Simple Liquids, North-Holland, Amsterdam, 1968.
-
(1968)
Physics of Simple Liquids
-
-
Temperley, H.N.V.1
Rowlinson, J.S.2
Rushbrooke, G.S.3
-
5
-
-
78751658223
-
-
N. B. Wilding (unpublished)
-
N. B. Wilding (unpublished)
-
-
-
-
6
-
-
78751660113
-
-
In the arguments of exponentials we shall generally absorb factors of kT ≡ 1/β into effective energy functions
-
In the arguments of exponentials we shall generally absorb factors of kT ≡ 1/β into effective energy functions.
-
-
-
-
10
-
-
5744249209
-
-
N. Metropolis, A.W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953)
-
(1953)
J. Chem. Phys.
, vol.21
, pp. 1087
-
-
Metropolis, N.1
Rosenbluth, A.W.2
Rosenbluth, M.N.3
Teller, A.H.4
Teller, E.5
-
11
-
-
78751652542
-
-
It would be more circumspect to say that the partition function cannot in general be naturally or usefully expressed as a canonical average since that average inevitably falls into the category for which canonical sampling is inadequate [13]
-
It would be more circumspect to say that the partition function cannot in general be naturally or usefully expressed as a canonical average since that average inevitably falls into the category for which canonical sampling is inadequate [13].
-
-
-
-
13
-
-
85086422511
-
-
0
-
0
-
-
-
-
14
-
-
78751652684
-
-
Throughout this section we use the notation introduced in Eq. (7) in which the phase label is absorbed into an extended macrostate label ℓ. The path defined by the set of macrostates (ℓ) may (and sometimes will) extend from one phase to another
-
Throughout this section we use the notation introduced in Eq. (7) in which the phase label is absorbed into an extended macrostate label ℓ. The path defined by the set of macrostates (ℓ) may (and sometimes will) extend from one phase to another.
-
-
-
-
15
-
-
78751656306
-
-
We shall refer to a field l and a macrovariable M as conjugate if the l-dependence of the configurational energy is of the form ℰ({q}, c; δ = ℰ({q}, c)- δ M ({q})
-
We shall refer to a field l and a macrovariable M as conjugate if the l-dependence of the configurational energy is of the form ℰ({q}, c; δ = ℰ({q}, c)- δ M ({q})
-
-
-
-
16
-
-
78751677792
-
-
It would be more conventional to refer to "densities," which are intensive. But we prefer to deal with their extensive counterparts, which we shall refer to as macrovariables. The preference reflects our focus on simulation studies which are necessarily conducted on systems of some given (finite) size
-
It would be more conventional to refer to "densities," which are intensive. But we prefer to deal with their extensive counterparts, which we shall refer to as macrovariables. The preference reflects our focus on simulation studies which are necessarily conducted on systems of some given (finite) size.
-
-
-
-
20
-
-
0002654663
-
-
J. Kertesz and I. Kondor, eds. Springer-Verlag, New York
-
E. Marinari, Optimized Monte Carlo Methods, in Advances in Computer Simulation, J. Kertesz and I. Kondor, eds., Springer-Verlag, New York, 1997
-
(1997)
Optimized Monte Carlo Methods, in Advances in Computer Simulation
-
-
Marinari, E.1
-
21
-
-
85086423190
-
-
2 ≡ α̃ c
-
2 ≡ α̃ c.
-
-
-
-
24
-
-
84953648015
-
-
A. P. Lyubartsev, A. A. Martsinovski, S. V. Shevkunov, and P. N. Vorontsov-Velyaminov, J. Chem. Phys. 96, 1776 (1992)
-
(1992)
J. Chem. Phys.
, vol.96
, pp. 1776
-
-
Lyubartsev, A.P.1
Martsinovski, A.A.2
Shevkunov, S.V.3
Vorontsov-Velyaminov, P.N.4
-
35
-
-
0009353101
-
-
H. Ogura, H. Matsuda, T. Ogawa, N. Ogita, and A. Ueda, Prog. Theor. Phys. 58, 419 (1977)
-
(1977)
Prog. Theor. Phys.
, vol.58
, pp. 419
-
-
Ogura, H.1
Matsuda, H.2
Ogawa, T.3
Ogita, N.4
Ueda, A.5
-
37
-
-
85044314629
-
-
P. G. Bolhuis, D. Frenkel, S.-C. Mau, and D. A. Huse, Nature 388, 235 (1997)
-
(1997)
Nature
, vol.388
, pp. 235
-
-
Bolhuis, P.G.1
Frenkel, D.2
Mau, S.-C.3
Huse, D.A.4
-
40
-
-
85086421976
-
-
hcp]/N
-
For hard spheres the Helmholtz free energy is purely entropic. Thus Table I shows the difference between the entropy per particle of the two phases, [Sfcc - Shcp]/N.
-
-
-
-
42
-
-
78751662234
-
-
Equation (10) shows that the logarithm of the probability ratio measures the free-energy difference, which is extensive
-
Equation (10) shows that the logarithm of the probability ratio measures the free-energy difference, which is extensive.
-
-
-
-
43
-
-
78751673828
-
-
In fact, HPT seems to require that all the points chosen for replicas lie suffiently close to coexistence that both phases have detectable signatures
-
In fact, HPT seems to require that all the points chosen for replicas lie suffiently close to coexistence that both phases have detectable signatures.
-
-
-
-
45
-
-
0039950749
-
-
B. Grossmann, M. L. Laursen, T. Trappenberg, and U. J. Wiese, Phys. Lett. B 293, 175 (1992
-
(1992)
Phys. Lett.
, vol.B 293
, pp. 175
-
-
Grossmann, B.1
Laursen, M.L.2
Trappenberg, T.3
Wiese, U.J.4
-
46
-
-
78751660417
-
-
Reference 44 and N. B. Wilding (unpublished
-
Reference 44 and N. B. Wilding (unpublished)
-
-
-
-
48
-
-
78751673960
-
-
Some of the results from Ref. 44 are included in the LJ phase diagram shown in Fig. 4
-
Some of the results from Ref. 44 are included in the LJ phase diagram shown in Fig. 4.
-
-
-
-
49
-
-
78751655296
-
-
Operationally we may regard a phase as "metastable" and assign it a "free energy" (in relation )to some other, also metastable) if the conditions for single-phase sampling [see Eq. (21) and accompanying discussion] are met
-
Operationally we may regard a phase as "metastable" and assign it a "free energy" (in relation to some other, also metastable) if the conditions for single-phase sampling [see Eq. (21) and accompanying discussion] are met.
-
-
-
-
50
-
-
78751662391
-
-
The configurations unearthed by the ES algorithm used in Lattice Switch studies of hard spheres (Section IV.D.2) have some distinctive features [48]
-
The configurations unearthed by the ES algorithm used in Lattice Switch studies of hard spheres (Section IV.D.2) have some distinctive features [48].)
-
-
-
-
53
-
-
78751675638
-
-
1/d the edge of the ddimensional simulation cube
-
When the interphase traverse proceeds by way of such two-phase configurations the free-energy barrier to be surmounted must scale with the area of the interface supporting two phases in equal measure. The probability of the ravine macrostates (and thus the probability of tunneling between the two phases at coexistence) must vanish as e-FI where the free-energy cost of the interface is of order FI ∼ δsLd-1, with δs the interface tension and L ∼ N1/d the edge of the ddimensional simulation cube.
-
-
-
-
54
-
-
78751668640
-
-
See, for example, Ref. 41
-
See, for example, Ref. 41.
-
-
-
-
55
-
-
78751674541
-
-
The method to be discussed in the next section belongs in this family; so does HPT, but less compellingly because of the limitations we have already touched on in Section IV.B.2
-
The method to be discussed in the next section belongs in this family; so does HPT, but less compellingly because of the limitations we have already touched on in Section IV.B.2.
-
-
-
-
56
-
-
78751651934
-
-
See Ref. 29, p. 176
-
See Ref. 29, p. 176.
-
-
-
-
57
-
-
78751658523
-
-
The traverse might work acceptably well if the dynamics of the interface between the two phases is favorable: systems with martensitic phase transitions may fall into this category: Z. Nishiyama, Martensitic Transformations, Academic Press, New York, 1978. Note also that the special case in which the structural phase transition involves no change of symmetry can be handled within the standard multicanonical framework [55]
-
The traverse might work acceptably well if the dynamics of the interface between the two phases is favorable: systems with martensitic phase transitions may fall into this category: Z. Nishiyama, Martensitic Transformations, Academic Press, New York, 1978. Note also that the special case in which the structural phase transition involves no change of symmetry can be handled within the standard multicanonical framework [55].
-
-
-
-
60
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-
41349121956
-
-
A. D. Bruce, A. N. Jackson, G. J. Ackland, and N. B. Wilding, Phys. Rev. E 65, 36710 (2002)
-
(2002)
Phys. Rev. e
, vol.65
, pp. 36710
-
-
Bruce, A.D.1
Jackson, A.N.2
Ackland, G.J.3
Wilding, N.B.4
-
62
-
-
78751658367
-
-
In general the partition function Eq. (2) should already incorporate a Jacobean reflecting the transformation from cartesian coordinates to the generalized coordinates {q}. It may always be absorbed into the configurational energy and we have adopted that convention
-
In general the partition function Eq. (2) should already incorporate a Jacobean reflecting the )transformation from cartesian coordinates to the generalized coordinates {q}. It may always be absorbed into the configurational energy and we have adopted that convention.
-
-
-
-
63
-
-
78751672469
-
-
The constraint is rarely made explict in MC studies: it is tacitly assumed that the conditions for "single-phase sampling" [Eq. (21) and accompanying discussion] are met
-
The constraint is rarely made explict in MC studies: it is tacitly assumed that the conditions for "single-phase sampling" [Eq. (21) and accompanying discussion] are met.
-
-
-
-
67
-
-
78751679034
-
-
One sees this more clearly when one views this relationship as the result of integrating Eq. (55)
-
One sees this more clearly when one views this relationship as the result of integrating Eq. (55)
-
-
-
-
68
-
-
78751670236
-
-
But a judicious choice of the representations chosen for the two phases, reflected in the transformation τ [Eq. (44)], can bring one closer to this attractive limit. See Refs. 70 and 71 and further remarks below
-
But a judicious choice of the representations chosen for the two phases, reflected in the transformation τ [Eq. (44)], can bring one closer to this attractive limit. See Refs. 70 and 71 and further remarks below.
-
-
-
-
69
-
-
78751653233
-
-
We use the term "lattice" rather loosely. The set of vectors {R→ }α identifies the orthodox lattice convoluted with the orthodox basis
-
We use the term "lattice" rather loosely. The set of vectors {R→ }α identifies the orthodox lattice convoluted with the orthodox basis.
-
-
-
-
70
-
-
78751678436
-
-
This will frequently be true for solid-solid phase behavior too; in the systems studied with Lattice Switch methods to date, the effects have proved rather small
-
This will frequently be true for solid-solid phase behavior too; in the systems studied with Lattice Switch methods to date, the effects have proved rather small.
-
-
-
-
74
-
-
78751657023
-
-
A. R. Acharya, A. D. Bruce, and G. J. Ackland, in preparation
-
A. R. Acharya, A. D. Bruce, and G. J. Ackland, in preparation.
-
-
-
-
80
-
-
84856128199
-
-
ibid 75 1461 1992
-
D. Möller and J. Fischer, Mol. Phys. 69, 463 (1990); ibid 75, 1461 (1992)
-
(1990)
Mol. Phys.
, vol.69
, pp. 463
-
-
Möller, D.1
Fischer, J.2
-
84
-
-
84957235540
-
-
See, for example, H. Falk, Am. J. Phys. 38, 858 (1970)
-
(1970)
Am. J. Phys.
, vol.38
, pp. 858
-
-
Falk, H.1
-
89
-
-
78751657636
-
-
A continuous space transformation like this can also be implemented in the lattice switch framework described in Section IV.D. By the same token, one can generally devise a continuous version of any LS transformation. Thus, for example, the obvious continuous counterpart of the fcc-hcp LS transformation depicted in Fig. 6 entails a gradual shear of the close-packed planes. Since the LS implementation remains always in the space of one or other of the crystalline structures, one might expect it to prove the safer choice. Where an explicit comparison of the two strategies has been made [87], this was indeed the conclusion
-
A continuous space transformation like this can also be implemented in the lattice switch framework described in Section IV.D. By the same token, one can generally devise a continuous version of any LS transformation. Thus, for example, the obvious continuous counterpart of the fcc-hcp LS transformation depicted in Fig. 6 entails a gradual shear of the close-packed planes. Since the LS implementation remains always in the space of one or other of the crystalline structures, one might expect it to prove the safer choice. Where an explicit comparison of the two strategies has been made [87], this was indeed the conclusion.
-
-
-
-
91
-
-
78751663182
-
-
We use {δ} to denote a set of physically different fields δ 2δ2 . . . . In contrast, [δ] (appearing in our discussion of paths) is shorthand for a set of different values δ(1) δ (1) . . . of some (particular) field δ. We use {M} and [M] in a similar way
-
We use {δ} to denote a set of physically different fields δ 2δ2 . . . . In contrast, [δ] (appearing in our discussion of paths) is shorthand for a set of different values δ(1) δ (1) . . . of some (particular) field δ. We use {M} and [M] in a similar way.
-
-
-
-
92
-
-
78751663736
-
-
It reduces to the familiar form with the macrovariables M1 and M2 chosen as respectively the enthalpy and the volume whose conjugate fields are 1=T and P=T
-
It reduces to the familiar form with the macrovariables M1 and M2 chosen as respectively the enthalpy and the volume whose conjugate fields are 1=T and P=T.
-
-
-
-
99
-
-
78751671877
-
-
Recall that knowing the weights that define a multicanonical distribution of some quantity M over some range is equivalent to knowing the true canonical M-distribution throughout the chosen range
-
Recall that knowing the weights that define a multicanonical distribution of some quantity M over some range is equivalent to knowing the true canonical M-distribution throughout the chosen range.
-
-
-
-
100
-
-
78751672016
-
-
For a review of FSS see Finite Size Scaling and Numerical Simulation of Statistical Systems, V. Privman, ed., World Scientific Publishing, Singapore, 1990
-
For a review of FSS see Finite Size Scaling and Numerical Simulation of Statistical Systems, V. Privman, ed., World Scientific Publishing, Singapore, 1990.
-
-
-
-
104
-
-
78751669844
-
-
As an immediate corollary, the field values that satisfy the equal-areas criterion will identify the coexistence curve of two such ensembles to within exponentially small corrections [95]
-
As an immediate corollary, the field values that satisfy the equal-areas criterion will identify the coexistence curve of two such ensembles to within exponentially small corrections [95].
-
-
-
-
105
-
-
0000315176
-
-
J. M. Polson, E. Trizac, S. Pronk, and D. Frenkel, J. Chem. Phys. 112, 5339 (2000)
-
(2000)
J. Chem. Phys.
, vol.112
, pp. 5339
-
-
Polson, J.M.1
Trizac, E.2
Pronk, S.3
Frenkel, D.4
-
106
-
-
0003829793
-
-
Oxford University Press, New York
-
J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. J. Newman, The Theory of Critical Phenomena: An Introduction to the Renormalization Group, Oxford University Press, New York, 1992.
-
(1992)
Newman, the Theory of Critical Phenomena: An Introduction to the Renormalization Group
-
-
Binney, J.J.1
Dowrick, N.J.2
Fisher, A.J.3
J, M.E.4
-
107
-
-
0002731173
-
-
See, for example, A. L. Sengers, R. Hocken, and J. V. Sengers, Phys. Today 30, 42 (1977)
-
(1977)
Phys. Today
, vol.30
, pp. 42
-
-
Sengers, A.L.1
Hocken, R.2
Sengers, J.V.3
-
110
-
-
12944333198
-
-
The treatment of scaling-field mixing in Ref. 100 has recently been corrected: M. E. Fisher and G Orkoulas, Phys. Rev. Lett. 85, 696 (2000)
-
(2000)
Phys. Rev. Lett.
, vol.85
, pp. 696
-
-
Fisher, M.E.1
Orkoulas, G.2
-
112
-
-
0037030028
-
-
In a number of recent papers the ideas outlined here have been developed to yield a framework in which the liquid-vapor coexistence curve can be tracked with remarkable precision deep into the critical region: E. Luijten, M. E. Fisher and A. Z. Panagiotopoulos, Phys. Rev. Lett. 88, 185701 (2002)
-
(2002)
Phys. Rev. Lett.
, vol.88
, pp. 185701
-
-
Luijten, E.1
Fisher, M.E.2
Panagiotopoulos, A.Z.3
-
113
-
-
78751669249
-
-
Y. C. Kim, M. E. Fisher and E Luitjen, cond-mat/0304032
-
Y. C. Kim, M. E. Fisher and E Luitjen, cond-mat/0304032.
-
-
-
-
119
-
-
0033733582
-
-
I. A. Rudnev, V. A. Kashurnikov, M. E. Gracheva, and O. A. Nikitenko, Physica C 332, 383 (2000)
-
(2000)
Physica C
, vol.332
, pp. 383
-
-
Rudnev, I.A.1
Kashurnikov, V.A.2
Gracheva, M.E.3
Nikitenko, O.A.4
-
122
-
-
0000354238
-
-
D. Alfe, G. A. De Wijs, G. Kresse, and M. J. Gillan Int. J. Quant. Chem. 77, 871 (2000)
-
(2000)
Int. J. Quant. Chem.
, vol.77
, pp. 871
-
-
Alfe, D.1
De Wijs, G.A.2
Kresse, G.3
Gillan, M.J.4
-
123
-
-
78751676495
-
-
Ecclesiastes 1:9. [The Holy Bible, King James Version, American Bible Society, New York, 1999).]
-
Ecclesiastes 1:9. [The Holy Bible, King James Version, American Bible Society, New York, 1999).]
-
-
-
-
126
-
-
0035506610
-
-
Phys. Rev. E, 64 056101 (2001)
-
(2001)
Phys. Rev. e
, vol.64
, pp. 056101
-
-
-
128
-
-
0035124659
-
-
C. Rickwardt, P. Nielaba, M. H. Muser, and K. Binder, Phys. Rev. B 63, 045204 (2001)
-
(2001)
Phys. Rev. B
, vol.63
, pp. 045204
-
-
Rickwardt, C.1
Nielaba, P.2
Muser, M.H.3
Binder, K.4
-
131
-
-
0001535689
-
-
S. Consta, N. B. Wilding, D. Frenkel, and Z. Alexandrowicz, J. Chem. Phys. 110, 3220 (1999)
-
(1999)
J. Chem. Phys.
, vol.110
, pp. 3220
-
-
Consta, S.1
Wilding, N.B.2
Frenkel, D.3
Alexandrowicz, Z.4
-
133
-
-
2142858485
-
-
D. P. Landau, S. P. Lewis, and H. B. Schttler, eds. Springer, Berlin
-
W. Kob, C. Brangian, T. Stuhn, and R. Yamamoto, in Computer Simulation Studies in Condensed Matter Physics XIII, D. P. Landau, S. P. Lewis, and H. B. Schttler, eds., Springer, Berlin, 2000.
-
(2000)
Computer Simulation Studies in Condensed Matter Physics XIII
-
-
Kob, W.1
Brangian, C.2
Stuhn, T.3
Yamamoto, R.4
-
134
-
-
78751665109
-
-
M. Kolesik, M. A. Novotny, and P. A. Rikvold, cond-mat 0207405
-
M. Kolesik, M. A. Novotny, and P. A. Rikvold, cond-mat 0207405.
-
-
-
-
135
-
-
78751664017
-
-
In this section we refer to E rather than its dimensionless counterpart ℰ ≡ βE since it seems advisable to make the measure of temperature β = 1/kT explicit
-
In this section we refer to E rather than its dimensionless counterpart ℰ ≡ βE since it seems advisable to make the measure of temperature β = 1/kT explicit.
-
-
-
-
138
-
-
78751658366
-
-
Different authors have made different choices of notation and adopted different sign conventions at this point. We adopt those of Ref. 122
-
Different authors have made different choices of notation and adopted different sign conventions at this point. We adopt those of Ref. 122.
-
-
-
-
140
-
-
78751656757
-
-
The constant k merely serves to assign a convenient lower (or upper) bound to the weights; the value chosen is absorbed in the normalization of the sampling distribution
-
The constant k merely serves to assign a convenient lower (or upper) bound to the weights; the value chosen is absorbed in the normalization of the sampling distribution.
-
-
-
-
143
-
-
78751656305
-
-
The WL scheme is terminated when the histogram is " sufficiently" flat and the weightmodification factor f is "sufficiently" close to unity
-
The WL scheme is terminated when the histogram is " sufficiently" flat and the weightmodification factor f is "sufficiently" close to unity.
-
-
-
-
146
-
-
78751670653
-
-
One may count the macrostate-transitions that are actually implemented, as in Ref. 55 or (retaining somewhat more information) store the acceptance probabilities of all attempted transitions, as in Ref. 126b
-
One may count the macrostate-transitions that are actually implemented, as in Ref. 55 or (retaining somewhat more information) store the acceptance probabilities of all attempted transitions, as in Ref. 126b.
-
-
-
-
147
-
-
0034341458
-
-
J. Stat. Phys. 98, 321 (2000)
-
(2000)
J. Stat. Phys.
, vol.98
, pp. 321
-
-
-
148
-
-
78751666159
-
-
There is a caveat here: The traverse through the interesting region needs to be slow enough to allow a rough local equilibrium in each macrostate to be established; this condition is satisfied relatively poorly at the outset (where the MC trajectory heads rapidly for the equilibrium states); but it gets better the closer the sampling distribution comes to the multicanonical limit; one requires no more than this
-
There is a caveat here: The traverse through the interesting region needs to be slow enough to allow a rough local equilibrium in each macrostate to be established; this condition is satisfied relatively poorly at the outset (where the MC trajectory heads rapidly for the equilibrium states); but it )gets better the closer the sampling distribution comes to the multicanonical limit; one requires no more than this.
-
-
-
-
154
-
-
78751652226
-
-
J. S. Wang and R. H. Swendsen, cond-mat/0104418
-
J. S. Wang and R. H. Swendsen, cond-mat/0104418.
-
-
-
-
155
-
-
78751667288
-
-
We subsume into the definitions of the macrovariables any parameters that do not have the credentials ("linearity") of the fields flg.)
-
We subsume into the definitions of the macrovariables any parameters that do not have the credentials ("linearity") of the fields flg.
-
-
-
-
156
-
-
78751673372
-
-
The unspecified constant in Eq. (B3) is prescribed by normalization
-
The unspecified constant in Eq. (B3) is prescribed by normalization.)
-
-
-
-
160
-
-
78751653086
-
-
The name seems to reflect no more than the fact that the resulting estimates of PDFs are as always based on (normalized) histograms accumulated in the sampling process
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The name seems to reflect no more than the fact that the resulting estimates of PDFs are as always based on (normalized) histograms accumulated in the sampling process.)
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161
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78751674695
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The observable Q is then a delta function that picks out prescribed values for the macrovariables in the setfMg
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The observable Q is then a delta function that picks out prescribed values for the macrovariables in the setfMg.
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162
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78751665393
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To do so, one must determine a set of weights that moderate the relative contributions of each histogram. There is more than a passing similarity here to the expanded ensemble framework discussed in Section III.C
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To do so, one must determine a set of weights that moderate the relative contributions of each histogram. There is more than a passing similarity here to the expanded ensemble framework discussed in Section III.C.
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