561 research outputs found
Finite-temperature ordering in a two-dimensional highly frustrated spin model
We investigate the classical counterpart of an effective Hamiltonian for a
strongly trimerized kagome lattice. Although the Hamiltonian only has a
discrete symmetry, the classical groundstate manifold has a continuous global
rotational symmetry. Two cases should be distinguished for the sign of the
exchange constant. In one case, the groundstate has a 120^\circ spin structure.
To determine the transition temperature, we perform Monte-Carlo simulations and
measure specific heat, the order parameter as well as the associated Binder
cumulant. In the other case, the classical groundstates are macroscopically
degenerate. A thermal order-by-disorder mechanism is predicted to select
another 120^\circ spin-structure. A finite but very small transition
temperature is detected by Monte-Carlo simulations using the exchange method.Comment: 11 pages including 9 figures, uses IOP style files; to appear in J.
Phys.: Condensed Matter (proceedings of HFM2006
Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
Frustration has proved to give rise to an extremely rich phenomenology in
both quantum and classical systems. The leading behavior of the system can
often be described by an effective model, where only the lowest-energy degrees
of freedom are considered. In this paper we study a system corresponding to the
strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic
field. It has been suggested that this system can be realized experimentally by
a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We
investigate the low-energy behavior of both the spin 1/2 quantum version and
the classical limit of this system by applying various techniques. We study in
parallel both signs of the coupling constant J since the two cases display
qualitative differences. One of the main peculiarities of the J>0 case is that,
at the classical level, there is an exponentially large manifold of
lowest-energy configurations. This renders the thermodynamics of the system
quite exotic and interesting in this case. For both cases, J>0 and J<0, a
finite-temperature phase transition with a breaking of the discrete dihedral
symmetry group D_6 of the model is present. For J<0, we find a transition
temperature T^<_c/|J| = 1.566 +/- 0.005, i.e., of order unity, as expected. We
then analyze the nature of the transition in this case. While we find no
evidence for a discontinuous transition, the interpretation as a continuous
phase transition yields very unusual critical exponents violating the
hyperscaling relation. By contrast, in the case J>0 the transition occurs at an
extremely low temperature, T^>_c ~= 0.0125 J. Presumably this low transition
temperature is connected with the fact that the low-temperature ordered state
of the system is established by an order-by-disorder mechanism in this case.Comment: 18 pages including 18 figures and 1 table; replaced in order to match
published version, most important change: added appendix with derivation of
Hamiltonian from spin-1/2 Heisenberg model on trimerized kagome lattic
On the universality of distribution of ranked cluster masses at critical percolation
The distribution of masses of clusters smaller than the infinite cluster is
evaluated at the percolation threshold. The clusters are ranked according to
their masses and the distribution of the scaled masses M for any
rank r shows a universal behaviour for different lattice sizes L (D is the
fractal dimension). For different ranks however, there is a universal
distribution function only in the large rank limit, i.e., (y and are defined in the text), where the
universal scaling function g is found to be Gaussian in nature.Comment: 4 pages, to appear in J. Phys.
Critical behaviour of the Rouse model for gelling polymers
It is shown that the traditionally accepted "Rouse values" for the critical
exponents at the gelation transition do not arise from the Rouse model for
gelling polymers. The true critical behaviour of the Rouse model for gelling
polymers is obtained from spectral properties of the connectivity matrix of the
fractal clusters that are formed by the molecules. The required spectral
properties are related to the return probability of a "blind ant"-random walk
on the critical percolating cluster. The resulting scaling relations express
the critical exponents of the shear-stress-relaxation function, and hence those
of the shear viscosity and of the first normal stress coefficient, in terms of
the spectral dimension of the critical percolating cluster and the
exponents and of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.
Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach
The present paper focuses on the order-disorder transition of an Ising model
on a self-similar lattice. We present a detailed numerical study, based on the
Monte Carlo method in conjunction with the finite size scaling method, of the
critical properties of the Ising model on some two dimensional deterministic
fractal lattices with different Hausdorff dimensions. Those with finite
ramification order do not display ordered phases at any finite temperature,
whereas the lattices with infinite connectivity show genuine critical behavior.
In particular we considered two Sierpinski carpets constructed using different
generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927..
and d_H=log 12/log 4 = 1.7924.., respectively.
The data show in a clear way the existence of an order-disorder transition at
finite temperature in both Sierpinski carpets.
By performing several Monte Carlo simulations at different temperatures and
on lattices of increasing size in conjunction with a finite size scaling
analysis, we were able to determine numerically the critical exponents in each
case and to provide an estimate of their errors.
Finally we considered the hyperscaling relation and found indications that it
holds, if one assumes that the relevant dimension in this case is the Hausdorff
dimension of the lattice.Comment: 21 pages, 7 figures; a new section has been added with results for a
second fractal; there are other minor change
A quantum Monte Carlo algorithm realizing an intrinsic relaxation
We propose a new quantum Monte Carlo algorithm which realizes a relaxation
intrinsic to the original quantum system. The Monte Carlo dynamics satisfies
the dynamic scaling relation and is independent of the Trotter
number. Finiteness of the Trotter number just appears as the finite-size
effect. An infinite Trotter number version of the algorithm is also formulated,
which enables us to observe a true relaxation of the original system. The
strategy of the algorithm is a compromise between the conventional worldline
local flip and the modern cluster loop flip. It is a local flip in the
real-space direction and is a cluster flip in the Trotter direction. The new
algorithm is tested by the transverse-field Ising model in two dimensions. An
accurate phase diagram is obtained.Comment: 9 pages, 4 figure
Three-dimensional Ising model in the fixed-magnetization ensemble: a Monte Carlo study
We study the three-dimensional Ising model at the critical point in the
fixed-magnetization ensemble, by means of the recently developed geometric
cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in
terms of microscopic spin-up and spin-down probabilities in a given
configuration of neighbors. In the thermodynamic limit, the relation between
this field and the magnetization reduces to the canonical relation M(h).
However, for finite systems, the relation is different. We establish a close
connection between this relation and the probability distribution of the
magnetization of a finite-size system in the canonical ensemble.Comment: 8 pages, 2 Postscript figures, uses RevTe
Monte Carlo computation of correlation times of independent relaxation modes at criticality
We investigate aspects of universality of Glauber critical dynamics in two
dimensions. We compute the critical exponent and numerically corroborate
its universality for three different models in the static Ising universality
class and for five independent relaxation modes. We also present evidence for
universality of amplitude ratios, which shows that, as far as dynamic behavior
is concerned, each model in a given universality class is characterized by a
single non-universal metric factor which determines the overall time scale.
This paper also discusses in detail the variational and projection methods that
are used to compute relaxation times with high accuracy
Magnetization switching in a Heisenberg model for small ferromagnetic particles
We investigate the thermally activated magnetization switching of small
ferromagnetic particles driven by an external magnetic field. For low uniaxial
anisotropy the spins can be expected to rotate coherently, while for sufficient
large anisotropy they should behave Ising-like, i.e., the switching should then
be due to nucleation. We study this crossover from coherent rotation to
nucleation for the classical three-dimensional Heisenberg model with a finite
anisotropy. The crossover is influenced by the size of the particle, the
strength of the driving magnetic field, and the anisotropy. We discuss the
relevant energy barriers which have to be overcome during the switching, and
find theoretical arguments which yield the energetically favorable reversal
mechanisms for given values of the quantities above. The results are confirmed
by Monte Carlo simulations of Heisenberg and Ising models.Comment: 8 pages, Revtex, 11 Figures include
Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet
We present a numerical study of the spin-1/2 bilayer Heisenberg
antiferromagnet with random interlayer dimer dilution. From the temperature
dependence of the uniform susceptibility and a scaling analysis of the spin
correlation length we deduce the ground state phase diagram as a function of
nonmagnetic impurity concentration p and bilayer coupling g. At the site
percolation threshold, there exists a multicritical point at small but nonzero
bilayer coupling g_m = 0.15(3). The magnetic properties of the single-layer
material La_2Cu_{1-p}(Zn,Mg)_pO_4 near the percolation threshold appear to be
controlled by the proximity to this new quantum critical point.Comment: minor changes, updated figure
- …