133 research outputs found
Equilibriumlike invaded cluster algorithm: critical exponents and dynamical properties
We present a detailed study of the Equilibriumlike invaded cluster algorithm
(EIC), recently proposed as an extension of the invaded cluster (IC) algorithm,
designed to drive the system to criticality while still preserving the
equilibrium ensemble. We perform extensive simulations on two special cases of
the Potts model and examine the precision of critical exponents by including
the leading corrections. We show that both thermal and magnetic critical
exponents can be obtained with high accuracy compared to the best available
results. The choice of the auxiliary parameters of the algorithm is discussed
in context of dynamical properties. We also discuss the relation to the
Li-Sokal bound for the dynamical exponent .Comment: 11 pages, 13 figures, accepted for publication in Phys. Rev.
Totally asymmetric exclusion process with long-range hopping
Generalization of the one-dimensional totally asymmetric exclusion process
(TASEP) with open boundary conditions in which particles are allowed to jump
sites ahead with the probability is studied by
Monte Carlo simulations and the domain-wall approach. For the
standard TASEP phase diagram is recovered, but the density profiles near the
transition lines display new features when . At the first-order
transition line, the domain-wall is localized and phase separation is observed.
In the maximum-current phase the profile has an algebraic decay with a
-dependent exponent. Within the regime, where the
transitions are found to be absent, analytical results in the continuum
mean-field approximation are derived in the limit .Comment: 10 pages, 9 figure
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
Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension
We study the model of deposition-evaporation of trimers on a line recently
introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the
model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain
with three-spin couplings given by H= \sum\displaylimits_i [(1 -
\sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+
+ h.c]. We study by exact numerical diagonalization of the variation of
the gap in the eigenvalue spectrum with the system size for rings of size up to
30. For the sector corresponding to the initial condition in which all sites
are empty, we find that the gap vanishes as where the gap exponent
is approximately . This model is equivalent to an interfacial
roughening model where the dynamical variables at each site are matrices. From
our estimate for the gap exponent we conclude that the model belongs to a new
universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included
Invaded cluster algorithm for a tricritical point in a diluted Potts model
The invaded cluster approach is extended to 2D Potts model with annealed
vacancies by using the random-cluster representation. Geometrical arguments are
used to propose the algorithm which converges to the tricritical point in the
two-dimensional parameter space spanned by temperature and the chemical
potential of vacancies. The tricritical point is identified as a simultaneous
onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of
"geometrical disorder cluster". The location of the tricritical point and the
concentration of vacancies for q = 1, 2, 3 are found to be in good agreement
with the best known results. Scaling properties of the percolating scaling
cluster and related critical exponents are also presented.Comment: 8 pages, 5 figure
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
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.
- …