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21.
It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs. 相似文献
22.
Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet. 相似文献
23.
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
24.
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
25.
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
26.
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
27.
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
28.
S. Redner 《Journal of statistical physics》1981,25(1):15-23
We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ
1, and akth neighboranti-ferromagnetic interactionJ
k
. WhenJ
k/J1=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F
N
(k)
=F
N–1
(k)
+F
N–k
(k)
. In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO. 相似文献
29.
C. Cammarota 《Journal of statistical physics》1981,25(1):143-152
A field theory model onR
2 in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in of the ground state energy, as 0, without using the cluster expansion.Supported in part by Consiglio Nazionale delle Ricerche. 相似文献
30.
A decorated lattice is suggested and the Ising model on it with three kinds
of interactions K1,
K2, and
K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-neighbor, and four-spin interactions, and the critical fixed point is found at
K1=0.5769,
K2=-0.0671, and
K3=0.3428, which determines the critical temperature of the system. It is also found that this system and
the regular square Ising lattice, and the eight-vertex model belong to the
same universality class. 相似文献