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31.
Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k
B
T
c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J1c/J=1.5004(20) together with the critical exponents
1
m
=0.237(5) and=0.461(15). 相似文献
32.
The amplitude
0 of the interfacial free energy per unit area (or surface tension) of the body-centered-cubic Ising model is found using a direct monte carlo simulation technique. The combination
2/kBTc, where is the correlation length, is shown to agree within the precision of the simulations with a previously reported estimate for the simple cubic lattice. Evidence is also presented for the universality of the finite-size scaling amplitude for the surface tension. 相似文献
33.
We present exact explicit expressions for the row spin-spin correlation functions
00
n0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for
00
n0. 相似文献
34.
James R. Kirkwood 《Journal of statistical physics》1984,37(3-4):407-417
We show the existence of a phase transition in the Ising model with transverse field for dimensionsv 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors. 相似文献
35.
We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ
0 andJ
1 with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–0
t](t), where 0 is a function of the stronger bond strengthJ
0 only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t
1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t
1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ
0, we find that ln (t) varies as –t
1/3(lnt)2/3 for large times. 相似文献
36.
Pierre Devillard 《Journal of statistical physics》1991,62(1-2):443-451
We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast
with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field. 相似文献
37.
J. M. G. Amaro de Matos A. E. Patrick V. A. Zagrebnov 《Journal of statistical physics》1992,66(1-2):139-164
An approach to the definition of infinite-volume Gibbs states for the (quenched) random-field Ising model is considered in the case of a Curie-Weiss ferromagnet. It turns out that these states are random quasi-free measures. They are random convex linear combinations of the free product-measures shifted by the corresponding effective mean fields. The conditional self-averaging property of the magnetization related to this randomness is also discussed.This paper is dedicated to Robert A. Minlos on the occasion of his 60th birthday. 相似文献
38.
The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional,
4, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well 4 model, the border model, and the double-well
4 model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions. 相似文献
39.
Ross Graham 《Journal of statistical physics》1982,29(2):177-183
We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field:
j
;
l
T
j
;
k
T
k
;
l
T
, and
j
;
l
T
k K
j
;
k
T
k
l
, whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02. 相似文献
40.
We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients Cn in the power series expansions of the magnetizationm in the form m(H)=1 + Cn(H-H
0
)n for various H0 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=Hsp(Ti < 0. 相似文献