47 research outputs found
Critical behaviour of the 1D q-state Potts model with long-range interactions
The critical behaviour of the one-dimensional q-state Potts model with
long-range interactions decaying with distance r as has been
studied in the wide range of parameters and . A transfer matrix has been constructed for a truncated range of
interactions for integer and continuous q, and finite range scaling has been
applied. Results for the phase diagram and the correlation length critical
exponent are presented.Comment: 20 pages plus 4 figures, Late
Critical behavior of the long-range Ising chain from the largest-cluster probability distribution
Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions
decaying with distance as are performed by applying the
Swendsen-Wang cluster algorithm with cumulative probabilities. The critical
behavior in the non-classical critical regime corresponding to is derived from the finite-size scaling analysis of the largest cluster.Comment: 4 pages, 2 figures, in RevTeX, to appear in Phys. Rev. E (Feb 2001
Quantum oscillations of the magnetic torque in the nodal-line Dirac semimetal ZrSiS
We report a study of quantum oscillations (QO) in the magnetic torque of the
nodal-line Dirac semimetal ZrSiS in the magnetic fields up to 35 T and the
temperature range from 40 K down to 2 K, enabling high resolution mapping of
the Fermi surface (FS) topology in the (Z-R-A) plane of the first
Brillouin zone (FBZ). It is found that the oscillatory part of the measured
magnetic torque signal consists of low frequency (LF) contributions
(frequencies up to 1000 T) and high frequency (HF) contributions (several
clusters of frequencies from 7-22 kT). Increased resolution and angle-resolved
measurements allow us to show that the high oscillation frequencies originate
from magnetic breakdown (MB) orbits involving clusters of individual
hole and electron pockets from the diamond shaped FS in the Z-R-A
plane. Analyzing the HF oscillations we have unequivocally shown that the QO
frequency from the dog-bone shaped Fermi pocket ( pocket) amounts
T. Our findings suggest that most of the frequencies in the LF
part of QO can also be explained by MB orbits when intraband tunneling in the
dog-bone shaped electron pocket is taken into account. Our results give
a new understanding of the novel properties of the FS of the nodal-line Dirac
semimetal ZrSiS and sister compounds
Short-time dynamics in the 1D long-range Potts model
We present numerical investigations of the short-time dynamics at criticality
in the 1D Potts model with power-law decaying interactions of the form
1/r^{1+sigma}. The scaling properties of the magnetization, autocorrelation
function and time correlations of the magnetization are studied. The dynamical
critical exponents theta' and z are derived in the cases q=2 and q=3 for
several values of the parameter belonging to the nontrivial critical
regime.Comment: 8 pages, 8 figures, minor changes - several typos fixed, one
reference change
Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
The q-state Potts model with long-range interactions that decay as 1/r^alpha
subjected to an uniform magnetic field on d-dimensional lattices is analized
for different values of q in the nonextensive regime (alpha between 0 and d).
We also consider the two dimensional antiferromagnetic Ising model with the
same type of interactions. The mean field solution and Monte Carlo calculations
for the equations of state for these models are compared. We show that, using a
derived scaling which properly describes the nonextensive thermodynamic
behaviour, both types of calculations show an excellent agreement in all the
cases here considered, except for alpha=d. These results allow us to extend to
nonextensive magnetic models a previous conjecture which states that the mean
field theory is exact for the Ising one.Comment: 10 pages, 4 figure
The Information Geometry of the One-Dimensional Potts Model
In various statistical-mechanical models the introduction of a metric onto
the space of parameters (e.g. the temperature variable, , and the
external field variable, , in the case of spin models) gives an alternative
perspective on the phase structure. For the one-dimensional Ising model the
scalar curvature, , of this metric can be calculated explicitly in
the thermodynamic limit and is found to be . This is positive definite and, for
physical fields and temperatures, diverges only at the zero-temperature,
zero-field ``critical point'' of the model.
In this note we calculate for the one-dimensional -state Potts
model, finding an expression of the form , where is the Potts
analogue of . This is no longer positive
definite, but once again it diverges only at the critical point in the space of
real parameters. We remark, however, that a naive analytic continuation to
complex field reveals a further divergence in the Ising and Potts curvatures at
the Lee-Yang edge.Comment: 9 pages + 4 eps figure
First-order transition in the one-dimensional three-state Potts model with long-range interactions
The first-order phase transition in the three-state Potts model with
long-range interactions decaying as has been examined by
numerical simulations using recently proposed Luijten-Bl\"ote algorithm. By
applying scaling arguments to the interface free energy, the Binder's
fourth-order cumulant, and the specific heat maximum, the change in the
character of the transition through variation of parameter was
studied.Comment: 6 pages (containing 5 figures), to appear in Phys. Rev.
Criticality in one dimension with inverse square-law potentials
It is demonstrated that the scaled order parameter for ferromagnetic Ising
and three-state Potts chains with inverse-square interactions exhibits a
universal critical jump, in analogy with the superfluid density in helium
films. Renormalization-group arguments are combined with numerical simulations
of systems containing up to one million lattice sites to accurately determine
the critical properties of these models. In strong contrast with earlier work,
compelling quantitative evidence for the Kosterlitz--Thouless-like character of
the phase transition is provided.Comment: To appear in Phys. Rev. Let
Reexamination of the long-range Potts model: a multicanonical approach
We investigate the critical behavior of the one-dimensional q-state Potts
model with long-range (LR) interaction , using a multicanonical
algorithm. The recursion scheme initially proposed by Berg is improved so as to
make it suitable for a large class of LR models with unequally spaced energy
levels. The choice of an efficient predictor and a reliable convergence
criterion is discussed. We obtain transition temperatures in the first-order
regime which are in far better agreement with mean-field predictions than in
previous Monte Carlo studies. By relying on the location of spinodal points and
resorting to scaling arguments, we determine the threshold value
separating the first- and second-order regimes to two-digit precision within
the range . We offer convincing numerical evidence supporting
$\sigma_c(q)Comment: 18 pages, 18 figure