arXiv subjects

Sabino José Ferreira

Publications and source records attributed to Sabino José Ferreira.

4 recordsLinked to original sources

arXiv1999

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang-Swendsen-Kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length $ξ\sim 5000$; the data are consistent with $ξ(β) = A e^{2β} β^p (1 + a_1 e^{-β} + ...)$ as $β\to\infty$, with $p \approx 1$. The staggered susceptibility behaves as $χ_{stagg} \sim ξ^{5/3}$. For q=4 the model is disordered ($ξ\ltapprox 2$) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.

cond-mat.stat-mech↗

arXiv1994

Finite-Size Scaling at $ξ/L \gg 1$

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $σ$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

hep-lat↗

arXiv1994

Antiferromagnetic Potts Models on the Square Lattice

We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Kotecký Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up to correlation length $ξ\sim 5000$; the data are consistent with $ξ(β) = A e^{2β} β(1 + a_1 e^{-β} + \ldots)$ as $β\to\infty$. For $q=4$ the model is disordered even at zero temperature.

hep-lat↗

arXiv1992

Multi-Grid Monte Carlo III. Two-Dimensional O(4)-Symmetric Nonlinear $σ$-Model

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric nonlinear $σ$-model [= SU(2) principal chiral model], on lattices up to $256 \times 256$. We find a dynamic critical exponent $z_{int,{\cal M}^2} = 0.60 \pm 0.07$ for the W-cycle and $z_{int,{\cal M}^2} = 1.13 \pm 0.11$ for the V-cycle, compared to $z_{int,{\cal M}^2} = 2.0 \pm 0.15$ for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a $256 \times 256$ lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

hep-lat↗