Amostragem entrópica tomográfica: aprimoramento e aplicações ao modelo de Ising antiferromagnético com campo externo e ao problema de flow shop scheduling

Abstract

We propose and test a new implementation of the tomographic entropic sampling (TES) algorithm based on the 1/t algorithm. We use t (with = 0, 1/2, 1 and 2) as a refinement factor of () (number of configurations in configuration class ). The rate of convergence is evaluated for the maximum of the specific heat, cmax, for the antiferromagnetic (AF) Ising model with external field on the square lattice, as well for the shop scheduling problem a typical subject of computer science and production engineering. We verify for both systems that convergence occurs for = 1; for = 1/2 there is also convergence, slower than for = 1 though. For = 0 and 2, however, there is no convergence. We simulated the AF Ising model for systems of sizes L = 10 to 30with L = 2; the critical line in the temperatureexternal field; critical exponents are evaluated via finite size scaling using TES for = 0 and 1. We also employed Metropolis sampling for larger sizes (L 320) in order to improve the estimates of critical points and exponents, as well the reduced fourth order Binder cumulant, along the critical line. Thesecritical estimates are in good agreement with their respective known literature values of the universality class of the two-dimensional Ising model. We also verify that the specific heat scales as ln L along the critical line, as expected.