ﻻ يوجد ملخص باللغة العربية
A finite array of $N$ globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling there is a clear separation of time scales of center of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the center of mass coordinate. We compute analytically the stationary probability and the moments of the center of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter $a_c(N)$ is determined. We identify a crossover from linear to square root scaling with increasing distance from $a_c$. The crossover point approaches $a_c$ in the limit $N to infty$ which reproduces previous results for infinite arrays. The results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on $N$ and is determined by the scaling behaviour near a fixed point of the stochastic flow.
We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and correlation size are significant quantities to characterize f
We consider the Dicke model in the ultra-strong coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers $N$ for bosonic and fermionic systems. We derive partition functions with degeneracy factors that
Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the the average current, the situation is much less understood for higher statistics. In this pa
We have studied the phase diagram of two capacitively coupled Josephson junction arrays with charging energy, $E_c$, and Josephson coupling energy, $E_J$. Our results are obtained using a path integral Quantum Monte Carlo algorithm. The parameter tha
Universal scaling laws form one of the central issues in physics. A non-standard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we foun