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1.
The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a
triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature
has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants.
A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice.
The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ
k
, the magnetization β and β
k
, the correlation length ν and ν
k
, as well as the Fisher exponents η and η
k
, have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated
antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior. 相似文献
2.
A. K. Murtazaev M. K. Ramazanov M. K. Badiev 《Bulletin of the Russian Academy of Sciences: Physics》2011,75(8):1042-1044
Critical properties of the 3D frustrated Heisenberg model on a triangle latticeare investigated using a replica Monte-Carlo
method that considers the interaction between next nearest neighbors. Static magnetic and chiral critical indices for heat
capacity α, susceptibility γ, γ
k
, magnetization β, β
k
, and correlation radius ν are calculated using the theory of finite-size scaling. 相似文献
3.
A. K. Murtazaev M. K. Ramazanov M. K. Badiev 《Bulletin of the Russian Academy of Sciences: Physics》2010,74(8):1138-1140
Using the Monte Carlo method, we study the critical properties of the three-dimensional frustrated Heisenberg model on a triangular
lattice with allowance for next-nearest neighbor interactions. Using the theory of finite-size scaling, we calculate the static
magnetic and chiral critical exponents of heat capacity α, susceptibility γ, γ
k
, magnetization β, β
k
, and correlation length ν. 相似文献
4.
The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated
by an infinite set of primitive divergences. The Hopf algebra of undecorated rooted trees, ℋ
R
, generated by a single primitive divergence, solves a universal problem in Hochschild cohomology. It has two nontrivial closed
Hopf subalgebras: the cocommutative subalgebra ℋladder of pure ladder diagrams and the Connes–Moscovici noncocommutative subalgebra ℋCM of noncommutative geometry. These three Hopf algebras admit a bigrading by n, the number of nodes, and an index k that specifies the degree of primitivity. In each case, we use iterations of the relevant coproduct to compute the dimensions
of subspaces with modest values of n and k and infer a simple generating procedure for the remainder. The results for ℋladder are familiar from the theory of partitions, while those for ℋCM involve novel transforms of partitions. Most beautiful is the bigrading of ℋ
R
, the largest of the three. Thanks to Sloane's superseeker, we discovered that it saturates all possible inequalities. We
prove this by using the universal Hochschild-closed one-cocycle B
+, which plugs one set of divergences into another, and by generalizing the concept of natural growth beyond that entailed
by the Connes–Moscovici case. We emphasize the yet greater challenge of handling the infinite set of decorations of realistic
quantum field theory.
Received: 31 January 2000 / Accepted: 7 July 2000 相似文献
5.
Suppose that A
1,…,A
N
are observables (selfadjoint matrices) and ρ is a state (density matrix). In this case the standard uncertainty principle, proved by Robertson, gives a bound for the
quantum generalized variance, namely for det {Cov
ρ
(A
j
,A
k
)}, using the commutators [A
j
,A
k
]; this bound is trivial when N is odd. Recently a different inequality of Robertson-type has been proved by the authors with the help of the theory of operator
monotone functions. In this case the bound makes use of the commutators [ρ,A
j
] and is non-trivial for any N. In the present paper we generalize this new result to the von Neumann algebra case. Nevertheless the proof appears to simplify
all the existing ones. 相似文献
6.
There are various situations in which it is natural to ask whether a given collection of k functions, ρ
j
(r
1,…,r
j
), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ
j
’s for this to be true. Our primary examples are X=ℝ
d
, X=ℤ
d
, and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently
small densities ρ
1(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when
X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example
in which a uniform density ρ and translation invariant ρ
2 are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established. 相似文献
7.
Beno?t?Collins Kenneth?J.?Dykema Francisco?Torres-Ayala 《Journal of statistical physics》2010,139(5):779-799
We show that the polynomial S
m,k
(A,B), that is the sum of all words in noncommuting variables A and B having length m and exactly k letters equal to B, is not equal to a sum of commutators and Hermitian squares in the algebra R〈X,Y〉, where X
2=A and Y
2=B, for all even values of m and k with 6≤k≤m−10, and also for (m,k)=(12,6). This leaves only the case (m,k)=(16,8) open. This topic is of interest in connection with the Lieb–Seiringer formulation of the Bessis–Moussa–Villani conjecture,
which asks whether Tr (S
m,k
(A,B))≥0 holds for all positive semidefinite matrices A and B. These results eliminate the possibility of using “descent + sum-of-squares” to prove the BMV conjecture. 相似文献
8.
It is shown that a second energy scale T
0 ≫ T
k arises in the Kondo problem. Perturbation theory is valid only in the region T > T
0. For this reason, the transition from weak to strong coupling occurs at temperatures much higher than the Kondo temperature
T
k.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 106–111 (25 July 1999) 相似文献
9.
Juraj Kumičák 《Czechoslovak Journal of Physics》1999,49(4):527-537
A model of 1/f noise is considered, based on moving averages of ordern. The coefficientsα
k
defining the model are calculated numerically using Seidel iteration which turns out to converge rapidly. The convergence
is independent ofn which seems to be caused by the fact that the nonlinear problem solved is defined by a self-similar matrix. The coefficientsα
k
appear to approach, with indefinitely growingn, valuesα
k
=1/√k and thus the model has a kind of Fourier invariance. Physical interpretation of the invariance is suggested as well
as of coefficientsα
k
describing long-range correlations. Fractal sets of dimensiond=2.5 are proposed to play certain role in explaining the latter.
This work was partly supported by the Scientific Grant Agency of the Ministry of Education of Slovak Republic (VEGA) under
the Grant No. 1/3143/96 and by the Slovak Literary Fund. 相似文献
10.
A. Nersessian 《Czechoslovak Journal of Physics》2000,50(11):1309-1315
We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk
N+a=kN−a, k2N
=0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk
i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system
are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
11.
We investigate SU(3)-periodic vortices in the self-dual Chern–Simons theory proposed by Dunne in [13, 15]. At the first admissible non-zero
energy level E= 2 π, and for each (broken and unbroken) vacuum state φ(0) of the system, we find a family of periodic vortices asymptotically gauge equivalent to φ(0), as the Chern–Simons coupling parameter k→ 0. At higher energy levels, we show the existence of multiple gauge distinct periodic vortices with at least one of them asymptotically gauge equivalent to the (broken) principal embedding vacuum, when k→ 0.
Received: 23 October 1999 / Accepted: 14 March 2000 相似文献
12.
Two-and three-body decays of γ(5S) into BB, BB*, B*B*, B
s
B
s
, B
s
B
s
*, and BB*π, B*B*π are evaluated using the theory developed earlier for dipion-bottomonium transitions. The theory contains only two parameters—vertex
masses M
br
and M
ω—known from the dipion spectra and width. Predicted values of Γtot(5S) and six partial widths Γ
k
(5S), k = BB, BB*, ... are in agreement with the experiment. The decay widths Γ5S
(πBB*) and Γ5S
(πB*B*) are also calculated and found to be on the order of 10 keV.
The text was submitted by the authors in English. 相似文献
13.
We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a
i
Δu
i
− f
j
(u, v), i = 1, …, k, with the diffusion coefficient a
i
> 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h
j
(u, v), j = k + 1, …, N, with zero diffusion. Here u = (u
1, …, u
k
) and v = (υ
k+1, …, υ
N
) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ
1, …, δ
k
), for the analogous reaction-diffusion systems having the terms δ
j
Δυ
j
− h
j
(u, v), j = k + 1, …, N, with small diffusion coefficients δ
j
⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+.
Dedicated to the memory of Vladimir Borovikov
Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500). 相似文献
14.
G. Parisi M. Ratiéville 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(2):229-237
We consider a class of random matching problems where the distance between two points has a probability law which, for a small
distance l, goes like lr. In the framework of the cavity method, in the limit of an infinite number of points, we derive equations for pk, the probability for some given point to be matched to its kth nearest neighbor in the optimal configuration. These equations are solved in two limiting cases: r = 0 -- where we recover p
k = 1/2k, as numerically conjectured by Houdayer et al. and recently rigorously proved by Aldous -- and r→ + ∞. For 0 < r < + ∞, we are not able to solve the equations analytically, but we compute the leading behavior of pk for large k.
Received 14 February 2001 相似文献
15.
M. G. Ryskin A. D. Martin V. A. Khoze 《The European Physical Journal C - Particles and Fields》2011,71(4):1617
We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement
with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between ‘hard’ and ‘soft’
interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the
data, these Monte Carlos need an additional infrared cutoff k
min with a value k
min ∼2–3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k
min . Using an alternative model which matches the ‘soft’ high-energy hadron interactions smoothly on to perturbative QCD at small
x, we demonstrate that this effective cutoff k
min is actually due to the strong absorption of low k
t
partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, ln k
t
, and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal
framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values
of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation
cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly
discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which
describe the high-energy pp and p[`(p)]p\bar{p} ‘soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related hard scattering data and from diffractive deep inelastic data looks encouraging. 相似文献
16.
On Noncommutative Multi-Solitons 总被引:2,自引:0,他引:2
Rajesh Gopakumar Matthew Headrick Marcus Spradlin 《Communications in Mathematical Physics》2003,233(2):355-381
We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The
existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic
energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ2)
k
/S
k
. We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ2/ℤ
k
, cylinder, and T
2
. However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli
space provides an explicit K?hler resolution of (ℝ4)
k
/S
k
. In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ
d
, which for d>2 (and k>3) is not smooth and can have multiple branches.
Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002
Communicated by R.H. Dijkgraaf 相似文献
17.
18.
A. H. Cai X. Xiong Y. Liu H. Chen W. K. An X. S. Li Y. Zhou Y. Luo 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,64(2):147-151
We propose expressions for the estimation of the isenthalpic temperature T
0 (T
0 = αT
m
, α is a semi-empirical parameter and 0 ⩽ α < 1, T
m
is the solidus temperature) and the Kauzmann temperature T
k
(T
k
= T
m
exp(α−1)) for glass forming alloys. It is found that T
k
estimated by T
k
= T
m
exp(α−1) is in agreement with that directly calculated from the heat capacity data, indicating that T
k
= T
m
exp(α − 1) can be used to estimate T
k
of glass forming alloys. T
0 estimated by T
0 = αT
m
, on the other hand, widely deviates from that of directly calculated from the heat capacity data. This suggests that the
enthalpy difference of the under-cooled liquid and the crystal might be a nonlinear function of the temperature below T
k
. Moreover, the Gibbs free energy difference ΔG is not sensitive to the deviation of α. 相似文献
19.
We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that
describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum E
LN(k) ∝ k
−5/3 must replace in future theory (e.g., in finding the quantum turbulence decay rate) the previously used spectrum E
KS(k) ∝ k
−7/5, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade. 相似文献
20.
We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having
anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r
2, u=4πξr
2, v
r=4πp
r
r
2, v
⊥=4πp
⊥
r
2[ρ, ξ(=−(1/2)F
14
F
14), p
r, p
⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas
ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field],
we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following
assumptions to solve the field equations (i) u=v
r=(a
2/2κ)r
n+2, v
⊥=k
1
v
r, w=k
2
v
r; a
2, n(>0), k
1, k
2 being constants with κ=((k
1+2)/3+k
2) and (ii) w+u=(b
2/2)r
n+2, u=v
r, v
⊥−v
r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as
well as physical variables for all values of n>0. Even though the second solution contains terms like k/r
2 since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing
it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior
Reissner-Nordstrom solution over a fixed boundary.
Dedicated to Prof. F A E Pirani. 相似文献