117 research outputs found
Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular XY Antiferromagnet: A Finite-Size Scaling Study
Histogram Monte-Carlo simulation results are presented for the magnetic-field
-- temperature phase diagram of the XY model on a stacked triangular lattice
with antiferromagnetic intraplane and ferromagnetic interplane interactions.
Finite-size scaling results at the various transition boundaries are consistent
with expectations based on symmetry arguments. Although a molecular-field
treatment of the Hamiltonian fails to reproduce the correct structure for the
phase diagram, it is demonstrated that a phenomenological Landau-type
free-energy model contains all the esstential features. These results serve to
complement and extend our earlier work [Phys. Rev. B {\bf 48}, 3840 (1993)].Comment: 5 pages (RevTex 3.0), 6 figures available upon request, CRPS 93-
Site Percolation and Phase Transitions in Two Dimensions
The properties of the pure-site clusters of spin models, i.e. the clusters
which are obtained by joining nearest-neighbour spins of the same sign, are
here investigated. In the Ising model in two dimensions it is known that such
clusters undergo a percolation transition exactly at the critical point. We
show that this result is valid for a wide class of bidimensional systems
undergoing a continuous magnetization transition. We provide numerical evidence
for discrete as well as for continuous spin models, including SU(N) lattice
gauge theories. The critical percolation exponents do not coincide with the
ones of the thermal transition, but they are the same for models belonging to
the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures,
references and comments adde
Helix vs. Sheet Formation in a Small Peptide
Segments with the amino acid sequence EKAYLRT appear in natural occurring
proteins both in -helices and -sheets. For this reason, we have
use this peptide to study how secondary structure formation in proteins depends
on the local environment. Our data rely on multicanonical Monte Carlo
simulations where the interactions among all atoms are taken into account.
Results in gas phase are compared with that in an implicit solvent. We find
that both in gas phase and solvated EKAYLRT forms an -helix when not
interacting with other molecules. However, in the vicinity of a -strand,
the peptide forms a -strand. Because of this change in secondary
structure our peptide may provide a simple model for the
transition that is supposedly related to the outbreak of Prion diseases and
similar illnesses.Comment: to appear in Physical Review
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.
Magnetization reversal times in the 2D Ising model
We present a theoretical framework which is generally applicable to the study
of time scales of activated processes in systems with Brownian type dynamics.
This framework is applied to a prototype system: magnetization reversal times
in the 2D Ising model. Direct simulation results for the magnetization reversal
times, spanning more than five orders of magnitude, are compared with
theoretical predictions; the two agree in most cases within 20%.Comment: 9 pages, 8 figure
Flat histogram simulation of lattice polymer systems
We demonstrate the use of a new algorithm called the Flat Histogram sampling
algorithm for the simulation of lattice polymer systems. Thermodynamics
properties, such as average energy or entropy and other physical quantities
such as end-to-end distance or radius of gyration can be easily calculated
using this method. Ground-state energy can also be determined. We also explore
the accuracy and limitations of this method.
Key words: Monte Carlo algorithms, flat histogram sampling, HP model, lattice
polymer systemsComment: 7 RevTeX two-column page
Simulation of Potts models with real q and no critical slowing down
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts
model for any real q>0. A single update is a random sequence of disordering and
deterministic moves, one for each link of the lattice. A disordering move
attributes a random value to the link, regardless of the state of the system,
while in a deterministic move this value is a state function. The relative
frequency of these moves depends on the two parameters q and beta. The
algorithm is not affected by critical slowing down and the dynamical critical
exponent z is exactly vanishing. We simulate in this way a 3D Potts model in
the range 2<q<3 for estimating the critical value q_c where the thermal
transition changes from second-order to first-order, and find q_c=2.620(5).Comment: 5 pages, 3 figures slightly extended version, to appear in Phys. Rev.
Histogram Monte Carlo study of next-nearest-neighbor Ising antiferromagnet on a stacked triangular lattice
Critical properties of the Ising model on a stacked triangular lattice, with
antiferromagnetic first and second-neighbor in-plane interactions, are studied
by extensive histogram Monte Carlo simulations. The results, in conjunction
with the recently determined phase diagram, strongly suggest that the
transition from the period-3 ordered state to the paramagnetic phase remains in
the xy universality class. This conclusion is in contrast with a previous
suggestion of mean-field tricritical behavior.Comment: 13 pages (RevTex 3.0), 10 figures available upon request, CRPS-93-0
Magnetic-Field Induced First-Order Transition in the Frustrated XY Model on a Stacked Triangular Lattice
The results of extensive Monte Carlo simulations of magnetic-field induced
transitions in the xy model on a stacked triangular lattice with
antiferromagnetic intraplane and ferromagnetic interplane interactions are
discussed. A low-field transition from the paramagnetic to a 3-state (Potts)
phase is found to be very weakly first order with behavior suggesting
tricriticality at zero field. In addition to clarifying some long-standing
ambiguity concerning the nature of this Potts-like transition, the present work
also serves to further our understanding of the critical behavior at ,
about which there has been much controversy.Comment: 10 pages (RevTex 3.0), 4 figures available upon request, CRPS-93-0
Critical behavior of the planar magnet model in three dimensions
We use a hybrid Monte Carlo algorithm in which a single-cluster update is
combined with the over-relaxation and Metropolis spin re-orientation algorithm.
Periodic boundary conditions were applied in all directions. We have calculated
the fourth-order cumulant in finite size lattices using the single-histogram
re-weighting method. Using finite-size scaling theory, we obtained the critical
temperature which is very different from that of the usual XY model. At the
critical temperature, we calculated the susceptibility and the magnetization on
lattices of size up to . Using finite-size scaling theory we accurately
determine the critical exponents of the model and find that =0.670(7),
=1.9696(37), and =0.515(2). Thus, we conclude that the
model belongs to the same universality class with the XY model, as expected.Comment: 11 pages, 5 figure
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