arXiv subjects

S. Jain

Publications and source records attributed to S. Jain.

26 records · Page 2Linked to original sources

arXiv1999

Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions

The non-equilibrium dynamics of the strongly diluted random-bond Ising model in two-dimensions (2d) is investigated numerically. The persistence probability, P(t), of spins which do not flip by time t is found to decay to a non-zero, dilution-dependent, value $P(\infty)$. We find that $p(t)=P(t)-P(\infty)$ decays exponentially to zero at large times. Furthermore, the fraction of spins which never flip is a monotonically increasing function over the range of bond-dilution considered. Our findings, which are consistent with a recent result of Newman and Stein, suggest that persistence in disordered and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the strength of the dilution present.

cond-mat.dis-nn↗

arXiv1999

Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-θ'}$, where $θ' = 0.420\pm 0.009$. The value of $θ'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-θ_d}$, where $θ_d = 0.63\pm 0.01$.

cond-mat.dis-nn↗

arXiv1998

The Two Dimensional XY Spin Glass with Ferromagnetic Next-Nearest-Neighbour Interactions

The random-bond XY spin glass with ferromagnetic next-nearest-neighbour interactions is studied on a square lattice by Monte Carlo simulations. We find strong evidence for a finite-temperature spin glass transition at $T_c\approx 1.1$. We also give estimates for the spin glass critical exponents for different values of the strength of the nearest-neighbour interaction. Our results are consistent with universal behaviour.

cond-mat.dis-nn↗

arXiv1997

Chiral Ordering in the Four-Dimensional XY Spin Glass

The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass in four dimensions is studied by Monte Carlo simulations. A chiral glass transition at $T_{cg}=0.90\pm 0.05$ is found by a finite-size scaling analysis of the results. The associated chiral correlation-length exponent is estimated to be $ν_{cg}=0.6\pm 0.1$ and $η_{cg}\sim 0.25$. The values for the chiral critical temperature and the exponents are very similar to those reported recently for the spin glass transition in this model. The results strongly suggest a simultaneous ordering of spin and chirality in four dimensions.

cond-mat.dis-nn↗

arXiv1996

The Four-Dimensional XY Spin Glass

The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite- size scaling analysis of the data leads to a finite temperature spin glass transition at $T_c=0.95\pm 0.15$. The critical exponents are estimated to be $ν_{sg}=0.70\pm 0.10$ and η_{sg}=-0.28\pm 0.38$. The results imply that the lower critical dimensionality for the XY spin glass is less than four.

cond-mat↗

arXiv1995

Anomalously slow relaxation in the diluted Ising model below the percolation threshold

The relaxational behaviour of the bond-diluted two-dimensional Ising model below the percolation threshold is studied using Monte Carlo techniques. The non-equilibrium decay of the magnetization,M(t), and the relaxation of the equilibrium spin-spin autocorrelation function, C(t), are monitored. The behaviour of both C(t) and M(t) is found to satisfy the Kohlrausch law of a stretched exponential with the same temperature-dependent exponent. The Kohlrausch exponent does not appear to depend on the bond concentration. The results indicate that we are not yet in the asymptotic regime, even when C(t) and M(t) are less than 10^{-4}.

cond-mat↗

arXiv1993

Baby universes in 2d quantum gravity

We investigate the fractal structure of $2d$ quantum gravity, both for pure gravity and for gravity coupled to multiple gaussian fields and for gravity coupled to Ising spins. The roughness of the surfaces is described in terms of baby universes and using numerical simulations we measure their distribution which is related to the string susceptibility exponent $\g_{string}$.

hep-th↗

arXiv1993

Observing 4D Baby Universes in Quantum Gravity

We measure the fractal structure of four dimensional simplicial quantum gravity by identifying so-called baby universes. This allows an easy determination of the critical exponent $\g$ connected to the entropy of four-dimensional manifolds.

hep-th↗