arXiv subjects

Bernard Derrida

Publications and source records attributed to Bernard Derrida.

58 records · Page 4Linked to original sources

arXiv1996

Distribution of domain sizes in the zero temperature Glauber dynamics of the 1 D Potts model

For the zero temperature Glauber dynamics of the $q$-state Potts model, we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one-species coagulation model ($A+A\rightarrow A$). In the long time limit, this distribution is universal and from its (complicated) exact expression, we extract its behavior in various regimes. Our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently. Considering the dynamics of domain walls as a reaction diffusion model $ A+A \to \ A $ with probability $ (q-2)/(q-1)$ and $A+A \to \emptyset $ with probability $1/(q-1)$, we calculate the pair correlation function in the long time regime.

cond-mat↗

arXiv1996

Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes

The fraction r(t) of spins which have never flipped up to time t is studied within a linear diffusion approximation to phase ordering. Numerical simulations show that, even in this simple context, r(t) decays with time like a power-law with a non-trival exponent $θ$ which depends on the space dimension. The local dynamics at a given point is a special case of a stationary gaussian process of known correlation function and the exponent $θ$ is shown to be determined by the asymptotic behavior of the probability distribution of intervals between consecutive zero-crossings of this process. An approximate way of computing this distribution is proposed, by taking the lengths of the intervals between successive zero-crossings as independent random variables. The approximation gives values of the exponent $θ$ in close agreement with the results of simulations.

cond-mat↗

arXiv1995

Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model

In the zero temperature Glauber dynamics of the ferromagnetic Ising or $q$-state Potts model, the size of domains is known to grow like $t^{1/2}$. Recent simulations have shown that the fraction $r(q,t)$ of spins which have never flipped up to time $t$ decays like a power law $r(q,t) \sim t^{-θ(q)}$ with a non-trivial dependence of the exponent $θ(q)$ on $q$ and on space dimension. By mapping the problem on an exactly soluble one-species coagulation model ($A+A\rightarrow A$), we obtain the exact expression of $θ(q)$ in dimension one.

hep-th↗

arXiv1994

The Unusual Universality of Branching Interfaces in Random Media

We study the criticality of a Potts interface by introducing a {\it froth} model which, unlike its SOS Ising counterpart, incorporates bubbles of different phases. The interface is fractal at the phase transition of a pure system. However, a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by {\it strong random bond disorder}. This implies a linear critical interface, and provides a mechanism for the conjectured equivalence of critical random Potts and Ising models.

cond-mat↗