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Register a new userCritical slowing down of topological modes
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We investigate the critical slowing down of the topological modes using local updating algorithms in lattice 2-d CP^(N-1) models. We show that the topological modes experience a critical slowing down that is much more severe than the one of the quasi-Gaussian modes relevant to the magnetic susceptibility, which is characterized by $tau_{rm mag} sim xi^z$ with $zapprox 2$. We argue that this may be a general feature of Monte Carlo simulations of lattice theories with non-trivial topological properties, such as QCD, as also suggested by recent Monte Carlo simulations of 4-d SU(N) lattice gauge theories.
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With the aim of studying the relevance and properties of critical slowing down in Monte Carlo simulations of lattice quantum field theories we carried out a high precision numerical study of the discretised two-dimensional CP^{N-1} model at N=10 using an over-heat bath algorithm. We identify critical slowing down in terms of slowly-evolving topological modes and present evidence that other observables couple to these slow modes. This coupling is found to reduce however as we increase the physical volume in which we simulate.
We investigate the response of a photonic gas interacting with a reservoir of pumped dye-molecules to quenches in the pump power. In addition to the expected dramatic critical slowing down of the equilibration time around phase transitions we find extremely slow equilibration even far away from phase transitions. This non-critical slowing down can be accounted for quantitatively by fierce competition among cavity modes for access to the molecular environment, and we provide a quantitative explanation for this non-critical slowing down.
We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations of the system state vector are driven by random variations of loads and intermittent renewable generation. In the vicinity of collapse the power system experiences so-called phenomenon of critical slowing-down characterized by slowing and simultaneous amplification of the system state vector fluctuations. In generic case of a co-dimension 1 bifurcation corresponding to the threshold of instability it is possible to extract a single mode of the system state vector responsible for this phenomenon. We characterize stochastic fluctuations of the system state vector using the formal perturbative expansion over the lowest (real) eigenvalue of the system power flow Jacobian and verify the resulting expressions for correlation functions of the state vector by direct numerical simulations. We conclude that the onset of critical slowing-down is a good marker of approach to the threshold of global instability. It can be straightforwardly detected from the analysis of single-node autostructure and autocorrelation functions of system state variables and thus does not require full observability of the grid.
Ultrasonic measurements have been carried out to investigate the critical dynamics of structural and superconducting transitions due to degenerate orbital bands in iron pnictide compounds with the formula Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. The attenuation coefficient $alpha_{mathrm{L}[110]}$ of the longitudinal ultrasonic wave for $(C_{11}+C_{12}+2C_{66})/2$ for $x = 0.036$ reveals the critical slowing down of the relaxation time around the structural transition at $T_mathrm{s} = 65$ K, which is caused by ferro-type ordering of the quadrupole $O_{x^2-y^2}$ coupled to the strain $varepsilon_{xy}$. The attenuation coefficient $alpha_{66}$ of the transverse ultrasonic wave for $C_{66}$ for $x = 0.071$ also exhibits the critical slowing down around the superconducting transition at $T_mathrm{SC} = 23$ K, which is caused by ferro-type ordering of the hexadecapole $H_z^alpha bigl( boldsymbol{r}_i, boldsymbol{r}_j bigr) = O_{xy}bigl( boldsymbol{r}_i bigr) O_{x^2 - y^2}bigl( boldsymbol{r}_j bigr) + O_{x^2 - y^2}bigl( boldsymbol{r}_i bigr) O_{xy}bigl( boldsymbol{r}_j bigr)$ of the bound two-electron state coupled to the rotation $omega_{xy}$. It is proposed that the hexadecapole ordering associated with the superconductivity brings about spontaneous rotation of the macroscopic superconducting state with respect to the host tetragonal lattice.
We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L=1024.
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