共查询到14条相似文献,搜索用时 15 毫秒
1.
R. J. Baxter 《Journal of statistical physics》1978,19(5):461-478
This paper concerns a square lattice, Ising-type model with interactions between the four spins at the corners of each face. These may include nearest and next-nearest-neighbor interactions, and interactions with a magnetic field. Provided the Hamiltonian is symmetric with respect to both row reversal and column reversal, a rapidly convergent sequence of variational approximations is obtained, giving the free energy and other thermodynamic properties. For the usual Ising model, the lowest such approximations are those of Bethe and of Kramers and Wannier. The method provides a new definition of corner transfer matrices. 相似文献
2.
A. Kalz A. Honecker S. Fuchs T. Pruschke 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,65(4):533-537
We restudy the phase diagram of the 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce
computational methods which allow us to calculate transition temperatures close to the criticalpoint at J2 = J1/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first
order formoderate J2 > J1/2. 相似文献
3.
V. Korepin N. Slavnov 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):555-557
We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional
Bose gas and XXZ Heisenberg quantum spin chain.
Received: 4 December 1997 / Accepted: 17 March 1998 相似文献
4.
A. Erdinç O. Canko E. Albayrak 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(4):521-529
The complete phase diagrams of the antiferromagnetic spin-2
Blume-Capel Ising system is studied on the Bethe lattice by the use
of exact recursion relations. In order to specify the states of the
system, i.e. the different spin configurations, the ground state
phase diagram is obtained on the (H/|J|, D/|J|) plane
corresponding to the reduced external magnetic and crystal fields,
respectively. As a result, the thermal change of the
order-parameters, the magnetisations belonging to the two sublattice
system, was investigated to obtain the full phase diagrams of the
system on the (H/|J|, kT/|J|) planes. The behavior of the
order-parameters with respect to the external magnetic field was
also studied for the given values of D/|J|. Besides the
interesting thermal and external magnetic field change of the
sublattice magnetisations, the system also exhibits interesting
critical behaviors including first- and second-order phase
transitions, therefore, triciritical points and the reentrant
behavior. The calculations are carried out for the coordination
number q=4, corresponding to the square lattice, only. 相似文献
5.
H. Chamati S. Romano 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(2):249-254
Generalized xy lattice spin models consist of
three-component unit vectors, associated with a D-dimensional
lattice (say
), parameterized by usual spherical
angles (θk,φk), and interacting via a ferromagnetic
potential restricted to nearest neighbours, of the form
here epsilon is a positive quantity setting energy and
temperature scales. The models were recently introduced,
and proven to support an ordering transition taking place
at finite temperature when D=3; in turn, this transition had been
investigated by different techniques for p=2,3,4, and found to
belong to the same universality class as the xy model (i.e. p=1).
More recently, it was rigorously proven that for
sufficiently large p the transition becomes first order. Here we present
a detailed analysis of the transitional properties of this
class of models for selected values of p.
For p=8 simulation results showed a second order phase
transition belonging to the xy class of universality;
they suggested tricritical behaviour for p=12,
and gave evidence of first-order transitions for both p=16 and p=20. 相似文献
6.
M. Casartelli N. Macellari A. Vezzani 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(2):149-156
A cylindrical Ising model between thermostats is used to explore the heat conduction for any temperature
interval. The standard Q2R and Creutz dynamics, previously used by Saito, Takesue and Miyashita, fail below the critical temperature,
limiting the analysis to high temperatures intervals. We introduce improved dynamics by removing limitations due to the chessboard-like
refresh, and by supplementing the Q2R rule with Kadanoff-Swift moves. These new dynamics not only prove highly efficient in
recovering old results in their domains of validity, but also allow exploration of steady heat transport between two arbitrary
temperatures, i.e. very far from equilibrium. From an ansatz avoiding references to quasi equilibrium or to local temperature,
and from comparison with numerical simulations, we can consistently define a generalized diffusivity. Its dependence on the
energy density may be evaluated without any recourse to the Green-Kubo formula. 相似文献
7.
O. Kapikranian B. Berche Yu. Holovatch 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(2):93-105
We present an analytic approach to study
concurrent influence of quenched non-magnetic site-dilution and
finiteness of the lattice on the 2D XY model. Two significant
deeply connected features of this spin model are: a special type
of ordering (quasi-long-range order) below a certain temperature
and a size-dependent mean value of magnetisation in the
low-temperature phase that goes to zero (according to the
Mermin-Wagner-Hohenberg theorem) in the thermodynamic limit. We
focus our attention on the asymptotic behaviour of the spin-spin
correlation function and the probability distribution of
magnetisation. The analytic approach is based on the spin-wave
approximation valid for the low-temperature regime and an
expansion in the parameters which characterise the deviation from
completely homogeneous configuration of impurities. We further
support the analytic considerations by Monte Carlo simulations
performed for different concentrations of impurities and compare
analytic and MC results. We present as the main quantitative
result of the work the exponent of the spin-spin correlation
function power law decay. It is non universal depending not only
on temperature as in the pure model but also on concentration of
magnetic sites. This exponent characterises also the vanishing of
magnetisation with increasing lattice size. 相似文献
8.
The distinct deviations from the Fermi-Dirac statistics ascertained recently at low temperatures for a one-dimensional, spinless fermionic discrete lattice gas with conserved number of noninteracting particles hopping on the non-degenerated, well-separated single-particle energy levels are studied in numerical and theoretical terms. The generalized distribution is derived in the formn(h)={Y
h
exp [(h–)]+1{su–1 valid even in the thermodynamic limit, when the discreteness of the energy levels is kept. This distribution demonstrates good agreement with the data obtained numerically both by the canonical partition function technique and by Monte Carlo simulation. 相似文献
9.
G. Parisi F. Tria 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(4):533-541
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington
Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry
breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average
connectivity (z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient
of the 1/z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this
annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the
temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry
breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking.
The 1/z expansion is well defined also in the zero temperature limit.
Received 15 July 2002 Published online 31 December 2002 相似文献
10.
S. Jain P. Buckley 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):133-136
Persistence is studied in a financial context by mapping the time
evolution of the values of the shares quoted on the London Financial
Times Stock Exchange 100 index (FTSE 100) onto Ising spins.
By following the time dependence
of the spins, we find evidence for power law decay of the proportion
of shares that remain either above or below their 'starting'
values. As a result, we estimate a persistence exponent for the
underlying financial market to be θf∼0.5. 相似文献
11.
E. Brézin C. De Dominicis 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(3):467-471
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting
correlation functions involve a superposition of different types of long distance behaviours. However the n = 0 limit allows one to discuss the renormalization group properties in spite of this phenomenon. The attraction of pairs
of replicas is enhanced under renormalization flow and no stable fixed point is found. Consequently, an instability occurs
in the paramagnetic region, before one reaches the Curie line, signalling the onset of replica symmetry breaking.
Received 28 July 2000 相似文献
12.
13.
K. Ebihara T. Watanabe 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,18(2):319-327
Since the droplet of the lattice-gas model with long-range interaction is not circular and is determined by the Wulff construction
due to surface tension anisotropy, a calculation method of the surface tension of the droplet is proposed in this paper. The
calculated surface tension is in good agreement with the surface tension measured by using the Laplace's formula in consideration
of the surface thickness.
Received 15 March 2000 and Received in final form 31 May 2000 相似文献
14.
M. Picco F. Ritort M. Sales 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(4):565-582
The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece
[2,3] which show that two of these parameters, G and G
c, take universal values in the . In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal
symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model
with and without a field and the Ising p-spin glass (p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite
volume limit. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore,
a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information
can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than
the Binder cumulant for T
c and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters
defined in terms of connected quantities are the proper ones to look at.
Received 20 September 2000 and Received in final form 10 January 2001 相似文献