0000000000174594
AUTHOR
Claudio Brangian
Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass
We use Monte Carlo simulations to study the static and dynamical properties of a Potts glass with infinite range Gaussian distributed exchange interactions for a broad range of temperature and system size up to N=2560 spins. The results are compatible with a critical divergence of the relaxation time tau at the theoretically predicted dynamical transition temperature T_D, tau \propto (T-T_D)^{-\Delta} with Delta \approx 2. For finite N a further power law at T=T_D is found, tau(T=T_D) \propto N^{z^\star} with z^\star \approx 1.5 and for T>T_D dynamical finite-size scaling seems to hold. The order parameter distribution P(q) is qualitatively compatible with the scenario of a first order glas…
Equilibrating Glassy Systems with Parallel Tempering
We discuss the efficiency of the so-called parallel tempering method to equilibrate glassy systems also at low temperatures. The main focus is on two structural glass models, SiO2 and a Lennard-Jones system, but we also investigate a fully connected 10 state Potts-glass. By calculating the mean squared displacement of a tagged particle and the spin-autocorrelation function, we find that for these three glass-formers the parallel tempering method is indeed able to generate, at low temperatures, new independent configurations at a rate which is O(100) times faster than more traditional algorithms, such as molecular dynamics and single spin flip Monte Carlo dynamics. In addition we find that t…
Evidence against a glass transition in the 10-state short range Potts glass
We present the results of Monte Carlo simulations of two different 10-state Potts glasses with random nearest neighbor interactions on a simple cubic lattice. In the first model the interactions come from a \pm J distribution and in the second model from a Gaussian one, and in both cases the first two moments of the distribution are chosen to be equal to J_0=-1 and Delta J=1. At low temperatures the spin autocorrelation function for the \pm J model relaxes in several steps whereas the one for the Gaussian model shows only one. In both systems the relaxation time increases like an Arrhenius law. Unlike the infinite range model, there are only very weak finite size effects and there is no evi…
Static and dynamic glass transitions in the 10-state Potts glass: What can Monte Carlo simulations contribute?
The p-state Potts glass with infinite range Gaussian interactions can be solved exactly in the thermodynamic limit and exhibits an unconventional phase behavior if p >4: A dynamical transition from ergodic to non-ergodic behavior at a temperature T D is followed by a first order transition at T 0 < T D, where a glass order parameter appears discontinuously, although the latent heat is zero. If one assumes that a similar scenario occurs for the structural glass transition as well (though with the singular behavior at T D rounded off), the p-state Potts glass should be a good test case to develop methods to deal with finite size effects for the static as well as the dynamic transition, and to…
The high-temperature dynamics of a mean-field Potts glass
Abstract We use Monte Carlo simulations to investigate the dynamic properties of the ten-state infinite-range Potts glass. By analyzing the spin autocorrelation function for system sizes up to N = 2560, we show that strong finite size effects are present around the predicted dynamic transition temperature. The autocorrelation function shows strong self-averaging at high temperatures, whereas close to the dynamic transition shows lack of self-averaging.
Ergodicity breaking in a mean field Potts glass: A Monte Carlo investigation
We use Monte Carlo simulations, single spin-flip as well as parallel tempering techniques to investigate the 10-state fully connected Potts glass for system sizes of up to N = 2560. We find that the α-relaxation shows a strong dependence on N and that for the system sizes considered the system remains ergodic even at temperatures below T D , the dynamical critical temperature for this model. However, if one uses the data for the finite size systems, such as the relaxation times or the time dependence of the spin autocorrelation function, and extrapolates them to the thermodynamic limit, one finds that they are indeed compatible with the results for N = ∞ (which are known from analytical cal…
Transitions between metastable states in silica clusters
Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems responsible for the anomalous specific heat and thermal conductivity in disordered solids with respect to crystals. By using a recently developed numerical algorithm, we study the potential energy landscape of silica clusters, taking as a starting point the location of first order saddle points. This allows us to find a great number of adjacent minima. We analyze the degree of cooperativity of these transitions and the connection of physical properties wi…
Dynamical susceptibility from simulations of a mean field Potts glass
Abstract We present results of the non-linear dynamic susceptibility χ(t) in a mean field Potts glass from simulations in a wide range of temperatures above the theoretically predicted dynamical transition, for various system sizes up to 2560 spins. χ(t) has a maximum, with a height that diverges like (T−TD)−α, with α≈1. The timescale t ∗ associated with this maximum also approaches a singularity, and we show that its behavior is compatible with the relaxation time of the standard time-dependent spin autocorrelation function, also with respect to finite size effects. We find that χ(t) for temperatures near the transition temperature TD satisfies a dynamical scaling property.
Energy and entropy barriers of two-level systems in argon clusters: An energy landscape approach
Abstract Free argon clusters containing up to 160 atoms have been studied by means of a numerical algorithm for finding thousands of adjacent minima connected through a first-order saddle point. Many minimum-saddle-minimum systems have been found to be good candidates for forming two-level systems. The ground state splitting has been evaluated by taking into account both energy and entropy barriers. The role of the latter in auenching or enhancing the ground state splitting is discussed with the aid of a simple model potential.