Green Function Simulation of Hamiltonian Lattice Models with Stochastic Reconfiguration

We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called Stochastic Reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge on the ground state is completely solved. In the $U(1)_2$ model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model dependent guiding functions for the random walkers.Comment: 14 pages, 5 PostScript Figures, RevTeX, two references adde

Scaling and universality in the aging kinetics of the two-dimensional clock model

We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_\chi}f(t/s)$, we find $a_\chi$ consistent with the value $a_\chi =0.28$ found in the two-dimensional Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures

Aging phenomena in critical semi-infinite systems

Nonequilibrium surface autocorrelation and autoresponse functions are studied numerically in semi-infinite critical systems in the dynamical scaling regime. Dynamical critical behaviour is examined for a nonconserved order parameter in semi-infinite two- and three-dimensional Ising models as well as in the Hilhorst-van Leeuwen model. The latter model permits a systematic study of surface aging phenomena, as the surface critical exponents change continuously as function of a model parameter. The scaling behaviour of surface two-time quantities is investigated and scaling functions are confronted with predictions coming from the theory of local scale invariance. Furthermore, surface fluctuation-dissipation ratios are computed and their asymptotic values are shown to depend on the values of surface critical exponents.Comment: 12 pages, figures included, version to appear in Phys. Rev.

Work fluctuations in quantum spin chains

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.Comment: 10 pages, 13 figure

Fluctuation-dissipation ratios in the dynamics of self-assembly

We consider two seemingly very different self-assembly processes: formation of viral capsids, and crystallization of sticky discs. At low temperatures, assembly is ineffective, since there are many metastable disordered states, which are a source of kinetic frustration. We use fluctuation-dissipation ratios to extract information about the degree of this frustration. We show that our analysis is a useful indicator of the long term fate of the system, based on the early stages of assembly.Comment: 8 pages, 6 figure

Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions

We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional, rather than activated, dynamics. We also look at the distribution of relaxation times among different samples, finding different results for the two q values. For q=3 the relative variance of the relaxation time tau at the critical point is finite. However, for q=24 this appears to diverge in the thermodynamic limit and it is ln(tau) which has a finite relative variance. We speculate that this difference occurs because the transition of the corresponding pure system is second order for q=3 but first order for q=24.Comment: 9 pages, 13 figures, final published versio

Probability distributions of the work in the 2D-Ising model

Probability distributions of the magnetic work are computed for the 2D Ising model by means of Monte Carlo simulations. The system is first prepared at equilibrium for three temperatures below, at and above the critical point. A magnetic field is then applied and grown linearly at different rates. Probability distributions of the work are stored and free energy differences computed using the Jarzynski equality. Consistency is checked and the dynamics of the system is analyzed. Free energies and dissipated works are reproduced with simple models. The critical exponent $\delta$ is estimated in an usual manner.Comment: 12 pages, 6 figures. Comments are welcom

Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below TCT_C

In order to check on a recent suggestion that local scale invariance [M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function in the kinetic Ising model with Glauber dynamics quenched to $T_C$ in $d=4$, where Gaussian behavior is expected to apply, and in the two other cases of the $d=2$ model quenched to $T_C$ and to below $T_C$, where instead deviations from Gaussian behavior are expected to appear. We find that in the $d=4$ case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the $d=2$ cases, both in the quench to $T_C$ and to below $T_C$, sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain $a=0.27 \pm 0.002$ for the scaling exponent of the response function in the $d=2$ Ising model quenched to below $T_C$, in agreement with previous results.Comment: 24 pages, 6 figures. Resubmitted version with improved discussions and figure

SPECT/CT registration with the DCC and MC simulations for SPECT imaging

publi Vincent Breto