12 research outputs found
A new approach to dynamic finite-size scaling
In this work we have considered the Taylor series expansion of the dynamic
scaling relation of the magnetization with respect to small initial
magnetization values in order to study the dynamic scaling behaviour of 2- and
3-dimensional Ising models. We have used the literature values of the critical
exponents and of the new dynamic exponent to observe the dynamic
finite-size scaling behaviour of the time evolution of the magnetization during
early stages of the Monte Carlo simulation. For 3-dimensional Ising Model we
have also presented that this method opens the possibility of calculating
and separately. Our results show good agreement with the literature
values. Measurements done on lattices with different sizes seem to give very
good scaling.Comment: Latex file with six figures. Accepted for publication in IJM
Storage Capacity of Extremely Diluted Hopfield Model
The storage capacity of the extremely diluted Hopfield Model is studied by
using Monte Carlo techniques. In this work, instead of diluting the synapses
according to a given distribution, the dilution of the synapses is obtained
systematically by retaining only the synapses with dominant contributions. It
is observed that by using the prescribed dilution method the critical storage
capacity of the system increases with decreasing number of synapses per neuron
reaching almost the value obtained from mean-field calculations. It is also
shown that the increase of the storage capacity of the diluted system depends
on the storage capacity of the fully connected Hopfield Model and the fraction
of the diluted synapses.Comment: Latex, 14 pages, 4 eps figure
Study of Cluster Fluctuations in Two-dimensional q-State Potts Model
The two-dimensional Potts Model with 2 to 10 states is studied using a
cluster algorithm to calculate fluctuations in cluster size as well as commonly
used quantities like equilibrium averages and the histograms for energy and the
order parameter. Results provide information about the variation of cluster
sizes depending on the temperature and the number of states. They also give
evidence for first-order transition when energy and the order parameter related
measurables are inconclusive on small size lattices.Comment: 12 pages, latex, four ps figures, submitted to Physica
A Study of Dynamic Finite Size Scaling Behavior of the Scaling Functions-Calculation of Dynamic Critical Index of Wolff Algorithm
In this work we have studied the dynamic scaling behavior of two scaling
functions and we have shown that scaling functions obey the dynamic finite size
scaling rules. Dynamic finite size scaling of scaling functions opens
possibilities for a wide range of applications. As an application we have
calculated the dynamic critical exponent () of Wolff's cluster algorithm for
2-, 3- and 4-dimensional Ising models. Configurations with vanishing initial
magnetization are chosen in order to avoid complications due to initial
magnetization. The observed dynamic finite size scaling behavior during early
stages of the Monte Carlo simulation yields for Wolff's cluster algorithm
for 2-, 3- and 4-dimensional Ising models with vanishing values which are
consistent with the values obtained from the autocorrelations. Especially, the
vanishing dynamic critical exponent we obtained for implies that the
Wolff algorithm is more efficient in eliminating critical slowing down in Monte
Carlo simulations than previously reported.Comment: Latex, 24 pages, 13 eps figures. Accepted for publication in Computer
Physics Communicatio
Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory
The renormalization functions involved in the determination of the
topological susceptibility in the SU(2) lattice gauge theory are extracted by
direct measurements, without relying on perturbation theory. The determination
exploits the phenomenon of critical slowing down to allow the separation of
perturbative and non-perturbative effects. The results are in good agreement
with perturbative computations.Comment: 12 pages + 4 figures (PostScript); report no. IFUP-TH 10/9
Analytical study of thermal entanglement in a two-dimensional J1-J2 model
We have investigated the ground-state and the thermal entanglement properties of a two-dimensional frustrated spin 1/2 cluster by calculating the pairwise concurrence and negativity. It is found that an increase in temperature can lead to an enhancement of pairwise entanglement for a certain range of the frustration parameter. We have, also, found that negativity is equal to the half of the concurrence for the model considered here. © 2006 Elsevier B.V. All rights reserved