ﻻ يوجد ملخص باللغة العربية
In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $sigma$ the critical value $C_{c}$ at which percolation occurs. The critical exponents in the range $0<sigma<1$ are reported and compared with mean-field and $varepsilon$-expansion results. Our analysis is in agreement, up to a numerical precision $approx 10^{-3}$, with the mean field result for the anomalous dimension $eta=2-sigma$, showing that there is no correction to $eta$ due to correlation effects.
In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time. Moreover, w
Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations follo
Finite-$N$ effects unavoidably drive the long-term evolution of long-range interacting $N$-body systems. The Balescu-Lenard kinetic equation generically describes this process sourced by ${1/N}$ effects but this kinetic operator exactly vanishes by s
We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field t
We investigate the nonequilibrium dynamics following a quench to zero temperature of the non-conserved Ising model with power-law decaying long-range interactions $propto 1/r^{d+sigma}$ in $d=2$ spatial dimensions. The zero-temperature coarsening is