ABSTRACT
We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.
ABSTRACT
We extend a previously proposed deposition model with two kinds of particle, considering the restricted solid-on-solid condition. The probability of incidence of particle C (A) is p (1-p). Aggregation is possible if the top of the column of incidence has a nearest neighbor A and if the difference in the heights of neighboring columns does not exceed 1. For any value of p>0, the deposit attains some static configuration, in which no deposition attempt is accepted. In 1+1 dimensions, the interface width has a limiting value W(s) approximately p(-eta), with eta=3/2, which is confirmed by numerical simulations. The dynamic scaling relation W(s)=p(-eta)f(tp(z)) is obtained in very large substrates, with z=eta.
ABSTRACT
We study the branched polymer growth model (BPGM) introduced by Lucena et al. [Phys. Rev. Lett. 72, 230 (1994)] in two dimensions. First the BPGM was simulated in very large lattices with concentrations of impurities q=0 and q=0.2. The scaling of the mass in chemical space gives accurate estimates of the critical branching probabilities b(c) and of the chemical dimensions Dc at criticality, improving previous results. Estimates of the fractal dimension D(F) at criticality are consistent with a universal value along the critical line. Our results for q=0 suggest small deviations of Dc and D(F) from the percolation values. We also simulated the BPGM in finite lattices of lengths between L=32 and L=512 for the same concentrations q. Using finite-size scaling techniques, we confirm the previous estimates of D(F) and the universality along the critical line, and obtain the correlation exponent nu=1.43+/-0.06. It proves that the BPGM is not in the same universality class of percolation in two dimensions. Finally, we simulate random walks on the critical polymers grown in very large lattices with q=0 and q=0.2, and obtain the random walk dimension Dw and the spectral dimension Ds. Dw is larger and Ds is smaller than the corresponding values in critical percolation clusters, due to the lower connectivity of the polymers. The scaling relation Ds=2D(F)/Dw is not satisfied, as observed in other tree-like structures.
