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1.
The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents 总被引:1,自引:0,他引:1
A. Klümper 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):677-685
We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary
external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at
very low temperatures (T/J=10-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent
is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate
and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.
Received: 12 February 1998 / Received in final form: 15 March 1998 / Accepted: 17 March 1998 相似文献
2.
W. Hofstetter W. Zwerger 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):751-756
We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility
at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also
to ferromagnetic quantum spin chains.
Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998 相似文献
3.
A. Benyoussef D. Dohmi A. El Kenz L. Peliti 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(4):503-510
Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition
in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals
to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that,
the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been
predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We
have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled
phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases
becomes first order.
Received: 3 December 1997 / Revised: 31 March 1998 / Accepted: 3 August 1998 相似文献
4.
D. Loison K.D. Schotte 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):735-743
The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group
(RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte-Carlo (MC) simulations which
favor a new universality class or a tricritical transition. We simulate by the Monte-Carlo method two models derived from
the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A
strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as
due to a fixed point in the complex plane. We review the experimental results in order to clarify the critical behavior observed.
Received: 18 February 1998 / Revised: 24 April 1998 / Accepted: 30 April 1998 相似文献
5.
6.
The influence of only partially screened Coulomb interactions on the phase diagram and the order parameter of quasi-one dimensional metals is investigated. Using a standard microscopic model, the free energy functional is derived by means of the heat kernel method. It is assumed that the Peierls gap and the mismatch are small compared to the band width and the reciprocal lattice vectors, respectively. Furthermore we neglect interchain to intrachain hopping elements. The resulting mean field phase diagram and the properties of the order parameter are discussed. We show in particular that the Coulomb forces are responsible for:a) a first-order transition between the incommensu-rate and the commensurate phase;b) only small deviations of the order parameter from a single plane wave over the entire incommensurate phase; andc) the approximate temperature independence of the wavelength of the modulation throughout the incommensurate phase. The possible relevance of these results for quasi-one dimensional systems exhibiting nonlinear conduction is pointed out. 相似文献
7.
M. Badehdah S. Bekhechi A. Benyoussef M. Touzani 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,4(4):431-440
A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J
2
<0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based
on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At
finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean
field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained
from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to
violate the ordinary universality hypothesis.
Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998 相似文献
8.
Y. Nishiyama 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(3):335-340
Ground-state phase diagram of the one-dimensional bond-random S=1 Heisenberg antiferromagnet is investigated by means of the loop-cluster-update quantum Monte-Carlo method. The random couplings
are drawn from a rectangular uniform distribution. We found that even in the case of extremely broad bond distribution, the
magnetic correlation decays exponentially, and the correlation length is hardly changed; namely, the Haldane phase continues
to be realized. This result is accordant with that of the exact-diagonalization study, whereas it might contradict the conclusion
of an analytic theory founded in a power-law bond distribution instead. The latter theory predicts that a second-order phase
transition occurs at a certain critical randomness, and the correlation length diverges for sufficiently strong randomness.
Received: 31 March 1998 / Revised and Accepted: 7 July 1998 相似文献
9.
A. Dutta J.K. Bhattacharjee B.K. Chakrabarti 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(1):97-103
We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists
of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at
a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point
in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation
technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d
u
= 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the
quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian
model by Fisher renormalisation.
Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998 相似文献
10.
D.M. Mastrogiuseppe M.E. Torio C.J. Gazza A.O. Dobry 《Physica B: Condensed Matter》2009,404(18):2805-2808
Going beyond a recently proposed microscopic model [D. Mastrogiuseppe, A. Dobry, arXiv:0810.3018v1] for the incommensurate transition in the spin-Peierls TiOX (X=Cl, Br) compounds, in the present work we start by studying the thermodynamics of the model with XY spins and adiabatic phonons. We find that the system enters an incommensurate phase by a first order transition at a low temperature Tc1. At a higher temperature Tc2 a continuous transition to a uniform phase is found. Furthermore, we study the magnetism in the incommensurate phase by density matrix renormalization group (DMRG) calculations on a one-dimensional Heisenberg model where the exchange is modulated by the incommensurate atomic position pattern. When the wave vector q of the modulation is near π, we find local magnetized zones (LMZ) in which spins abandon their singlets as a result of the domain walls induced by the modulated distortion. When q moves far away enough from π, the LMZ disappear and the system develops incommensurate magnetic correlations induced by the structure. We discuss the relevance of this result regarding previous and future experiments in TiOCl. 相似文献
11.
P. Germain M. Laguës 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(4):497-505
We study the electronic and magnetic structure of the undoped ideal two and three-leg ladder cuprates by assuming a moderate
on site coulombic repulsion. This analysis is an extension of the Fermi liquids studies proposed for the CuO2 plane in view to explain the high Tc superconductivity and the competition with the antiferromagnetic phase. At zero doping, the quasi-one-dimensionality of the
structure results in SDW correlations with different (commensurate) vectors according to the number of legs, which contrasts
with the predictions made from the Heisenberg model. At mean field, and for n = 3 (Sr2Cu3O5), we predict a magnetic ordered state, detected by μSr and NMR measurements with critical temperatures consistent with our
assumptions on the physical parameters, the modulation vector being .The presence of several bands at the Fermi level explains why there is no observable gap in the static susceptibility measurements.
For n = 2, we predict a gap consistent with experimental Curie susceptibility. But the expected magnetic instability is detected
only in La2Cu2O5, where the interladder coupling is stronger. In every case the one-dimensional van Hove singularities are far from the Fermi
level, making difficult the obtaining of high Tc superconductivity.
Received 3 June 1998 相似文献
12.
C. Schuster U. Eckern 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):395-402
In order to study the effect of interaction and lattice distortion on quantum coherence in one-dimensional Fermi systems,
we calculate the ground state energy and the phase sensitivity of a ring of interacting spinless fermions on a dimerized lattice.
Our numerical DMRG studies, in which we keep up to 1000 states for systems of about 100 sites, are supplemented by analytical
considerations using bosonization techniques. We find a delocalized phase for an attractive interaction, which differs from
that obtained for random lattice distortions. The extension of this delocalized phase depends strongly on the dimerization
induced modification of the interaction. Taking into account the harmonic lattice energy, we find a dimerized ground state
for a repulsive interaction only. The dimerization is suppressed at half filling, when the correlation gap becomes large.
Received: 11 February 1998 / Revised: 1st April 1998 / Accepted: 30 April 1998 相似文献
13.
Comparing mean field and Euclidean matching problems 总被引:1,自引:0,他引:1
J. Houdayer J.H. Boutet de Monvel O.C. Martin 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(3):383-393
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered
systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems.
Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered.
We first study a mean field model taking the link lengths between points to be independent random variables. For this model
we find perfect agreement with the results of a replica calculation, and give a conjecture. Then we study the case where the
points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that
the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d
2
). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among
k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than
at . However, we argue that the dimensional dependence of the Euclidean model's energy density is non-perturbative, i.e., it is beyond all orders in k of the expansion in k-link correlations.
Received: 1st December 1997 / Revised: 6 May 1998 / Accepted: 30 June 1998 相似文献
14.
A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation
corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model
in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two
dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations
are locally enhanced at the low-U sites.
Received 27 April 1998 and Received in final form 13 August 1998 相似文献
15.
Precursor phenomena of displacive transformation have been studied by optical and transmission electron microscope observation and X-ray diffraction of Ti–(50???x)Ni–xFe (x?=?2,?4,?6,?8 in at.%) alloys. We found that a Ti–44Ni–6Fe alloy exhibits a second-order-like incommensurate–commensurate transition without latent heat and discontinuity in lattice parameters. In other words, diffuse scatterings appear in an electron diffraction pattern at an incommensurate position on cooling; they move gradually towards 1/3? 110? as the temperature decreases and lock into the commensurate position at 180?K. The commensurate phase is not expanded along one of the ? 111? directions, unlike the R-phase formed by a first-order transformation in Ti–48Ni–2Fe and Ti–46Ni–4Fe alloys. In addition, the commensurate phase shows a nanoscale domain-like structure, which is inherited from the incommensurate state of the parent phase. Thus, the anomalies in physical properties observed in the incommensurate state are most likely the precursor phenomena of the commensurate phase in the Ti–44Ni–6Fe alloy. In the case of a Ti–42Ni–8Fe alloy, the incommensurate state remains even at 19?K. 相似文献
16.
M. Benakli M. Gabay W.M. Saslow 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,1(2):197-204
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate
structures. We present a method which allows to deal with this problem, both for ground state and for critical properties:
it combines fluctuating boundary conditions and specific histogram techniques. Our approach concerns classical systems possessing
a continuous symmetry as well as quantum systems. In particular, current-current correlation functions, which probe large
scale coherence of the states, can be accurately evaluated. We illustrate our method on a frustrated two dimensional XY model.
Received: 9 September 1997 / Revised: 17 October 1997 / Accepted: 3 November 1997 相似文献
17.
B. Lobe W. Janke K. Binder 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(2):283-291
We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the
p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor
couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions,
this enabled us to determine the critical coupling Kc and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the
model and present a careful comparison with previous estimates for special values of p and d.
Received: 25 May 1998 / Revised and Accepted: 11 August 1998 相似文献
18.
Y. Nishiyama 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,9(2):215-223
Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated
by means of the exact-diagonalization method for the system sizes up to L=5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate,
with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as and z=2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical
response function) is expressed in terms of the continued-fraction form consisting of Lanczos tri-diagonal elements. Thereby,
we estimate the universal DC conductivity as .
Received 19 August 1998 相似文献
19.
20.
M. Dudzinski J. Sznajd 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):745-750
The ground state properties of S
=2 ferromagnets with isotropic Heisenberg exchange (J) and single-ion cubic anisotropy (D) are studied. The perturbation theory for is used to find an effective Hamiltonian up to the fourth order for 1, 2 and 3 dimensions. It is shown that in opposition
to the MFA prediction there is the quadrupolar long range order at T
= 0 in the non-magnetic state of the system without a quadrupolar type of interaction. The effect is a consequence of the quantum
nature of the model.
Received: 19 February 1998 / Accepted: 17 March 1998 相似文献