Related papers: Monte Carlo results for three-dimensional self-avo…
We present computer simulations of anomalous diffusion, $< r^2(t) > \sim a t^{1-\delta}$, in two dimensions. The Monte Carlo calculations are in excellent agreement with previous renormalization group calculations. Interestingly, use of a…
The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our…
We discuss different approaches for studying the influence of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalisation group calculations provide quite accurate results. Experiments carried out on…
We use a large cell Monte Carlo Renormalization procedure, to compute the critical exponents of a system of growing linear polymers. We simulate the growth of non-intersecting chains in large MC cells. Dense regions where chains get in each…
Monte Carlo simulations alone could not clarify the corrections to scaling for the size-dependent p_c(L) above the upper critical dimension. Including the previous series estimate for the bulk threshold $p_c(\infty)$ gives preference for…
We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
We present an extension of the so-called cumulant crossing method which is used for determination of critical point in Monte Carlo simulations.The new method uses linear combination of several different order-parameter moments and almost…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
We introduce several infinite families of new critical exponents for the random-cluster model and present scaling arguments relating them to the k-arm exponents. We then present Monte Carlo simulations confirming these predictions. These…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
We compute the critical exponents $\nu$, $\eta$ and $\omega$ of $O(N)$ models for various values of $N$ by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually…
We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in…
We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $\sigma$-model at correlation lengths $\xi$ up to $\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte…
We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
We have tested the leading correction-to-scaling exponent omega in O(n)-symmetric models on a three-dimensional lattice by analysing the recent Monte Carlo (MC) data. We have found that the effective critical exponent, estimated at finite…
We present a new Monte Carlo methodology for the accurate estimation of the distribution of the sum of dependent log-normal random variables. The methodology delivers statistically unbiased estimators for three distributional quantities of…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…