Critical exponents of ferromagnetic Ising model on fractal lattices

We review the value of the critical exponents $\nu^{-1}$, $\beta/\nu$, and $\gamma/\nu$ of ferromagnetic Ising model on fractal lattices of Hausdorff dimension between one and three. They are obtained by Monte Carlo simulation with the help of Wolff algorithm. The results are accurate enough to show that the hyperscaling law $d_f=2\beta/\nu+\gamma/\nu$ is satisfied in non-integer dimension. Nevertheless, the discrepancy between the simulation results and the $\epsilon$-expansion studies suggests that the strong universality should be adapted for the fractal lattices.Comment: 5 pages, 1 figure, 1 table; conference article for the sixth international school "Symmetry and Structural Properties of Condensed Matter (SSPCM'2000)" in Polan

Comment on "Critical and slow dynamics in a bulk metallic glass exhibiting strong random magnetic anisotropy" [Appl. Phys. Lett. 92, 011923 (2008)]

In this comment, by using Monte Carlo simulation, we show that the perpendicular shift of hysteresis loops reported in the commented work is nothing special but simply due to the fact that the range of field does not surpass the reversible field beyond which the two branches of the loop merge. If the reversible field is exceeded, the shift is no longer observed. Moreover, we point out that even using a small range of field, the shift will not be observed if the observation time is long enough for the reversible field to drop within the range.Comment: 2 pages, 2 figures, accepted for publication in Applied Physics Letters Volume 94, Issue 15, Issue date 13 April 200

Mangetic phase transition for three-dimensional Heisenberg weak random anisotropy model: Monte Carlo study

Magnetic phase transition (MPT) to magnetic quasi-long-range order (QLRO) phase in a three-dimensional Heisenberg weak (D/J=4) random anisotropy (RA) model is investigated by Monte Carlo simulation. The isotropic and cubic distributions of RA axes are considered for simple-cubic-lattice systems. Finite-size scaling analysis shows that the critical couplings for the former and latter are K_c= 0.70435(2) and K_c=0.70998(4), respectively. While the critical exponent 1/\nu =1.40824(0) is the same for both cases. A second-order MPT to the QLRO phase is therefore evidenced to be possible in favor with the existence of the QLRO predicted by recent functional renormalization group theories.Comment: 9 pages, 3 figures. to be appeared in Journal of Applied Physics Volume 105 Issue 7 on April 1, 200

An ac field probe for the magnetic ordering of magnets with random anisotropy

A Monte Carlo simulation is carried out to investigate the magnetic ordering in magnets with random anisotropy (RA). Our results show peculiar similarities to recent experiments that the real part of ac susceptibility presents two peaks for weak RA and only one for strong RA regardless of glassy critical dynamics manifested for them. We demonstrate that the thermodynamic nature of the low-temperature peak is a ferromagnetic-like dynamic phase transition to quasi-long range order (QLRO) for the former. Our simulation, therefore, is able to be incorporated with the experiments to help clarify the existence of the QLRO theoretically predicted so far.Comment: 10 pages, 4 figures, to appear in Appl. Phys. Lett. volume 95, Issue 22, Isue date: 30 November 200

Effect of chain stiffness on ion distributions around a polyelectrolyte in multivalent salt solutions

Ion distributions in dilute polyelectrolyte solutions are studied by means of Langevin dynamics simulations. We show that the distributions depend on the conformation of a chain while the conformation is determined by the chain stiffness and the salt concentration. We observe that the monovalent counterions originally condensed on a chain can be replaced by the multivalent ones dissociated from the added salt due to strong electrostatic interaction. These newly condensed ions give an important impact on the chain structure. At low and at high salt concentrations, the conformation of a semiflexible chain is rodlike. The ion distributions show similarity to those for a rigid chain, but difference to those for a flexible chain whose conformation is a coil. In the mid-salt region, the flexible chain and the semiflexible chain collapse but the collapsed chain structures are, respectively, disordered and ordered structures. The ion distributions hence show different profiles for these three chain stiffness with the curves for the semiflexible chain lying between those for the flexible and the rigid chains. The number of the condensed multivalent counterions, as well as the effective chain charge, also shows similar behavior, demonstrating a direct connection with the chain morphology. Moreover, we find that the condensed multivalent counterions form triplets with two adjacent monomers and are localized on the chain axis at intermediate salt concentration when the chain stiffness is semiflexible or rigid. The microscopic information obtained here provides valuable insight to the phenomena of DNA condensation and is very useful for researchers to develop new models.Comment: 28 pages, 10 figures, accepted for publication in JC

MuseGAN: Multi-track Sequential Generative Adversarial Networks for Symbolic Music Generation and Accompaniment

Generating music has a few notable differences from generating images and videos. First, music is an art of time, necessitating a temporal model. Second, music is usually composed of multiple instruments/tracks with their own temporal dynamics, but collectively they unfold over time interdependently. Lastly, musical notes are often grouped into chords, arpeggios or melodies in polyphonic music, and thereby introducing a chronological ordering of notes is not naturally suitable. In this paper, we propose three models for symbolic multi-track music generation under the framework of generative adversarial networks (GANs). The three models, which differ in the underlying assumptions and accordingly the network architectures, are referred to as the jamming model, the composer model and the hybrid model. We trained the proposed models on a dataset of over one hundred thousand bars of rock music and applied them to generate piano-rolls of five tracks: bass, drums, guitar, piano and strings. A few intra-track and inter-track objective metrics are also proposed to evaluate the generative results, in addition to a subjective user study. We show that our models can generate coherent music of four bars right from scratch (i.e. without human inputs). We also extend our models to human-AI cooperative music generation: given a specific track composed by human, we can generate four additional tracks to accompany it. All code, the dataset and the rendered audio samples are available at https://salu133445.github.io/musegan/ .Comment: to appear at AAAI 201