419 research outputs found
Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions
We study the effects of frozen boundaries in a Monte Carlo simulation near a
first order phase transition. Recent theoretical analysis of the dynamics of
first order phase transitions has enabled to state the scaling laws governing
the critical regime of the transition. We check these new scaling laws
performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In
particular, our results support a pseudo-critical beta finite-size scaling of
the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d +
d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not
coincide with the latent heat analytically derived for the same model if
periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure
Surface critical exponents at a uniaxial Lifshitz point
Using Monte Carlo techniques, the surface critical behaviour of
three-dimensional semi-infinite ANNNI models with different surface
orientations with respect to the axis of competing interactions is
investigated. Special attention is thereby paid to the surface criticality at
the bulk uniaxial Lifshitz point encountered in this model. The presented Monte
Carlo results show that the mean-field description of semi-infinite ANNNI
models is qualitatively correct. Lifshitz point surface critical exponents at
the ordinary transition are found to depend on the surface orientation. At the
special transition point, however, no clear dependency of the critical
exponents on the surface orientation is revealed. The values of the surface
critical exponents presented in this study are the first estimates available
beyond mean-field theory.Comment: 10 pages, 7 figures include
Kinetics in one-dimensional lattice gas and Ising models from time-dependent density functional theory
Time-dependent density functional theory, proposed recently in the context of
atomic diffusion and non-equilibrium processes in solids, is tested against
Monte Carlo simulation. In order to assess the basic approximation of that
theory, the representation of non-equilibrium states by a local equilibrium
distribution function, we focus on one-dimensional lattice models, where all
equilibrium properties can be worked exactly from the known free energy as a
functional of the density. This functional determines the thermodynamic driving
forces away from equilibrium. In our studies of the interfacial kinetics of
atomic hopping and spin relaxation, we find excellent agreement with
simulations, suggesting that the method is useful also for treating more
complex problems.Comment: 8 pages, 5 figures, submitted to Phys. Rev.
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
Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models
We use Monte Carlo techniques and analytical methods to study the phase
diagram of multicomponent Widom-Rowlinson models on a square lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M between two and
six there is a direct transition from the gas phase at z < z_d (M) to a demixed
phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there
is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In
this phase, which is driven by entropy, particles, independent of species,
preferentially occupy one of the sublattices, i.e. spatial symmetry but not
particle symmetry is broken. The transition at z_d(M) appears to be first order
for M \geq 5 putting it in the Potts model universality class. For large M the
transition between the crystalline and demixed phase at z_d(M) can be proven to
be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to
behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one
component hard square lattice gas has a transition, and to be always of the
Ising type. Explicit calculations for the Bethe lattice with the coordination
number q=4 give results similar to those for the square lattice except that the
transition at z_d(M) becomes first order at M>2. This happens for all q,
consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure
Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
The distributions of singular thermodynamic quantities in an ensemble
of quenched random samples of linear size at the critical point are
studied by Monte Carlo in two models. Our results confirm predictions of
Aharony and Harris based on Renormalization group considerations. For an
Ashkin-Teller model with strong but irrelevant bond randomness we find that the
relative squared width, , of is weakly self averaging. , where is the specific heat exponent and is the
correlation length exponent of the pure model fixed point governing the
transition. For the site dilute Ising model on a cubic lattice, known to be
governed by a random fixed point, we find that tends to a universal
constant independent of the amount of dilution (no self averaging). However
this constant is different for canonical and grand canonical disorder. We study
the distribution of the pseudo-critical temperatures of the ensemble
defined as the temperatures of the maximum susceptibility of each sample. We
find that its variance scales as and NOT as
R_\chi\sim 70R_\chi (T_c)\chiT_c(i,l)m_i(T_c,l)T_c(i,l)(T-T_c(i,l))/T_c$. This function is found to be universal and to behave
similarly to pure systems.Comment: 31 pages, 17 figures, submitted to Phys. Rev.
Computational Nuclear Physics and Post Hartree-Fock Methods
We present a computational approach to infinite nuclear matter employing
Hartree-Fock theory, many-body perturbation theory and coupled cluster theory.
These lectures are closely linked with those of chapters 9, 10 and 11 and serve
as input for the correlation functions employed in Monte Carlo calculations in
chapter 9, the in-medium similarity renormalization group theory of dense
fermionic systems of chapter 10 and the Green's function approach in chapter
11. We provide extensive code examples and benchmark calculations, allowing
thereby an eventual reader to start writing her/his own codes. We start with an
object-oriented serial code and end with discussions on strategies for porting
the code to present and planned high-performance computing facilities.Comment: 82 pages, to appear in Lecture Notes in Physics (Springer), "An
advanced course in computational nuclear physics: Bridging the scales from
quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck,
Editor
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
When the two-dimensional random-bond Ising model is represented as a
noninteracting fermion problem, it has the same symmetries as an ensemble of
random matrices known as class D. A nonlinear sigma model analysis of the
latter in two dimensions has previously led to the prediction of a metallic
phase, in which the fermion eigenstates at zero energy are extended. In this
paper we argue that such behavior cannot occur in the random-bond Ising model,
by showing that the Ising spin correlations in the metallic phase violate the
bound on such correlations that results from the reality of the Ising
couplings. Some types of disorder in spinless or spin-polarized p-wave
superconductors and paired fractional quantum Hall states allow a mapping onto
an Ising model with real but correlated bonds, and hence a metallic phase is
not possible there either. It is further argued that vortex disorder, which is
generic in the fractional quantum Hall applications, destroys the ordered or
weak-pairing phase, in which nonabelian statistics is obtained in the pure
case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe
Lattice-switch Monte Carlo
We present a Monte Carlo method for the direct evaluation of the difference
between the free energies of two crystal structures. The method is built on a
lattice-switch transformation that maps a configuration of one structure onto a
candidate configuration of the other by `switching' one set of lattice vectors
for the other, while keeping the displacements with respect to the lattice
sites constant. The sampling of the displacement configurations is biased,
multicanonically, to favor paths leading to `gateway' arrangements for which
the Monte Carlo switch to the candidate configuration will be accepted. The
configurations of both structures can then be efficiently sampled in a single
process, and the difference between their free energies evaluated from their
measured probabilities. We explore and exploit the method in the context of
extensive studies of systems of hard spheres. We show that the efficiency of
the method is controlled by the extent to which the switch conserves correlated
microstructure. We also show how, microscopically, the procedure works: the
system finds gateway arrangements which fulfill the sampling bias
intelligently. We establish, with high precision, the differences between the
free energies of the two close packed structures (fcc and hcp) in both the
constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.
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