Hysteresis behavior in current-driven stationary resonance induced by nonlinearity in the coupled sine-Gordon equation

Recently novel current-driven resonant states characterized by the $\pi$-phase kinks were proposed in the coupled sine-Gordon equation. In these states hysteresis behavior is observed with respect to the application process of current, and such behavior is due to nonlinearity in the sine term. Varying strength of the sine term, there exists a critical strength for the hysteresis behavior and the amplitude of the sine term coincides with the applied current at the critical strength.Comment: 3 pages, 3 figures, RevTeX

Stationary phase-kink states and dynamical phase transitions controlled by surface impedance in THz wave emission from intrinsic Josephson junctions

As possible states to characterize THz wave emission from intrinsic Josephson junctions without external fields, the McCumber-like state and $\pi$-phase-kink state have been proposed. In the present article it is numerically shown that both states are stationary according to the bias current $J$ and surface impedance $Z$. The McCumber-like state is stable for low $J$ and small $Z$. For higher $J$, the $\pi$-phase-kink state accompanied with symmetry breaking along the c axis is stable even for Z=1, though strong emission in the vicinity of cavity resonance points only takes place for larger $Z$. Different emission behaviors for Z=1 and 10 are precisely compared. The dynamical phase diagram for $1 \le Z \le 10$ and the optimal value of $Z$ for the strongest emission are also evaluated.Comment: 4 pages, 8 figures, RevTe

New quantum Monte Carlo study of quantum critical phenomena with Trotter-number-dependent finite-size scaling and non-equilibrium relaxation

We propose a new efficient scheme for the quantum Monte Carlo study of quantum critical phenomena in quantum spin systems. Rieger and Young's Trotter-number-dependent finite-size scaling in quantum spin systems and Ito {\it et al.}'s evaluation of the transition point with the non-equilibrium relaxation in classical spin systems are combined and generalized. That is, only one Trotter number and one inverse temperature proportional to system sizes are taken for each system size, and the transition point of the transformed classical spin model is estimated as the point at which the order parameter shows power-law decay. The present scheme is confirmed by the determination of the critical phenomenon of the one-dimensional $S=1/2$ asymmetric XY model in the ground state. The estimates of the transition point and the critical exponents $\beta$, $\gamma$ and $\nu$ are in good agreement with the exact solutions. The dynamical critical exponent is also estimated as {\mit \Delta}=2.14(I4(Jpm 0.06, which is consistent with that of the two-dimensional Ising model.Comment: 15 pages, 17 Postscript figures, LaTeX, J. Phys. A in pres

New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms

Nonequilibrium relaxation behaviors in the Ising model on a square lattice based on the Wolff algorithm are totally different from those based on local-update algorithms. In particular, the critical relaxation is described by the stretched-exponential decay. We propose a novel scaling procedure to connect nonequilibrium and equilibrium behaviors continuously, and find that the stretched-exponential scaling region in the Wolff algorithm is as wide as the power-law scaling region in local-update algorithms. We also find that relaxation to the spontaneous magnetization in the ordered phase is characterized by the exponential decay, not the stretched-exponential decay based on local-update algorithms.Comment: J. Phys. Soc. Jpn. 83 (2014) in press; 5 pages, 5 figures, jpsj3.cls Ver.1.

Energy landscape and shear modulus of interlayer Josephson vortex systems

The ground state of interlayer Josephson vortex systems is investigated on the basis of a simplified Lawrence-Doniach model in which spatial dependence of the gauge field and the amplitude of superconducting order parameter is not taken into account. Energy landscape is drawn with respect to the in-plane field, the period of insulating layers including Josephson vortices, and the shift from the aligned vortex lattice. The energy landscape has a multi-valley structure and ground-state configurations correspond to bifurcation points of the valleys. In the high-field region, the shear modulus becomes independent of field and its anisotropy dependence is given by $c_{66}\propto \gamma^{-4}$.Comment: 4 pages, 7 figures (2 gif figures not in the text); RevTe

Crossover behaviors in liquid region of vortex states above a critical point caused by point defects

Vortex states in high-$T_{\rm c}$ superconductors with point defects are studied by large-scale Monte Carlo simulations of the three-dimensional frustrated XY model. A critical point is observed on the first-order phase boundary between the vortex slush and vortex liquid phases. A step-like anomaly of the specific heat is detected in simulations of finite systems, similar to an experimental observation [F.~Bouquet {\it et al.}, Nature (London) {\bf 411}, 448 (2001)]. However, it diminishes with increasing system size, and the number and size distribution of thermally-excited vortex loops show continuous behaviors around this anomaly. Therefore, the present study suggests a crossover rather than a thermodynamic phase transition above the critical point.Comment: 4 pages, 9 eps figures, using RevTeX

Quantum Hopfield Model

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the ratio of the number of stored patterns to the system size)-$\Delta$ (the strength of the transverse field) phase diagram of this model in the ground state resembles the $\alpha$-$T$ phase diagram of the Hopfield model quantitatively, within the replica-symmetric and static approximations. This fact suggests that quantum fluctuations play quite similar roles to thermal fluctuations in neural networks as long as macroscopic properties are concerned.Comment: 11 pages, 1 compressed/uuencoded postscript figure, revte

Evidence of first-order transition between vortex glass and Bragg glass phases in high-TcT_{\rm c} superconductors with point pins: Monte Carlo simulations

Phase transition between the vortex glass and the Bragg glass phases in high-$T_{\rm c}$ superconductors in $\vec{B}\parallel\vec{c}$ is studied by Monte Carlo simulations in the presence of point pins. A finite latent heat and a $\delta$-function peak of the specific heat are observed, which clearly indicates that this is a thermodynamic first-order phase transition. Values of the entropy jump and the Lindemann number are consistent with those of melting transitions. A large jump of the inter-layer phase difference is consistent with the recent Josephson plasma resonance experiment of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$ by Gaifullin {\it et al.}Comment: 4 pages, 5 Postscript figures, uses revtex.st

Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D $q=5$ Potts model, and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the 3D and 4D XY models and in the 2D $q$-state Potts models for $2 \le q \le 4$, and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D $q=5$ and $6$ Potts models, and propose a quantitative criterion on "weakness" of the first-order phase transition.Comment: 4 pages, 6 figures, RevTeX

Cluster nonequilibrium relaxation in Ising models observed with the Binder ratio

The Binder ratios exhibit discrepancy from the Gaussian behavior of the magnetic cumulants, and their size independence at the critical point has been widely utilized in numerical studies of critical phenomena. In the present article we reformulate the nonequilibrium relaxation (NER) analysis in cluster algorithms using the $(2,1)$-Binder ratio, and apply this scheme to the two- and three-dimensional Ising models. Although the stretched-exponential relaxation behavior at the critical point is not explicitly observed in this quantity, we find that there exists a logarithmic finite-size scaling formula which can be related with a similar formula recently derived in cluster NER of the correlation length, and that the formula enables precise evaluation of the critical point and the stretched-exponential relaxation exponent $\sigma$. Physical background of this novel behavior is explained by the simulation-time dependence of the distribution function of magnetization in two dimensions and temperature dependence of $\sigma$ obtained from magnetization in three dimensions.Comment: 8 pages, 20 figures, RevTeX4.1 (revision only for format of figures