Nonequilibrium relaxation method

Abstract

The nonequilibrium relaxation (NER) method is a numerical technique to analyse equilibrium phase transitions. One can estimate the transition point and critical exponents calculating relaxations of order parameter and fluctuations in NER processes from nonequilibrium initial states to the equilibrium ones. It is applied to the second-order transition as well as the first-order one; the precise estimation of transition temperature for the latter case is achieved with the mixed phase initialization technique. Since the equilibration is not necessary in the simulation, one can analyse systems with large sizes which can be recognized as in the thermodynamic limit up to the observation time. This leads to the analysis being more efficient for slowly relaxing systems with frustrations and randomness. It can be extended to the Kosterlitz-Thouless transition and the spin glass transition cases by the use of the finite-time scaling analysis. It is also extended to quantum systems.

Single-crystalP31NMR studies of the frustrated square-lattice compoundPb2(Nath1, Furukawa2, Borsa3 et al. 2009Phys. Rev. B8320640View full textAdd to dashboardCite

“…The ␤ values expected for different spin and lattice dimensionalities are listed in Table II. 47,[51][52][53][54] If we assume that the experimental ␤ value of Ϸ0.23 obtained above from the measurements on the single crystal is due to critical fluctuations, then the ␤ value is closer to the 2D XY than the three-dimensional ͑3D͒ models although the ordering is suggested to be a 3D order from the powder neutron diffraction measurements. 28 We suggest that our data are not sufficiently close to T N to reflect 3D critical behavior.…”

Critical Langevin dynamics of the O(N) Ginzburg–Landau model with correlated noise

“…In the white-noise-dominated case we choose τ = l 2 γ w and a similar argument yields the white-noise result z = 2 + η w . In short, 15) and therefore one needs to calculate η w and η γ in order to determine z.…”

Opinion Formation in the Kinetic Exchange Models

“…(3), such that an agent only exchange opinion with one of its two nearest neighbors. Then they study the non-equilibrium relaxation, using the non-equilibrium relaxation technique proposed in [31]. In nonequlibrium relaxation the simulation is started from a fully ordered state.…”