Eur. Phys. J. B 50, 63-67 (2006)
https://doi.org/10.1140/epjb/e2006-00032-2

Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions

Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, GR 15784 Zografos, Athens, Greece

Corresponding author: ^a amalakis@cc.uoa.gr

Received: 12 October 2005
Revised: 22 November 2005
Published online: 8 February 2006

Abstract

We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the Metropolis algorithm. We consider interactions in the range where superantiferromagnetic (SAF) order appears at low temperatures. A recent prediction of a first-order transition along a certain range (0.5–1.2) of the interaction ratio (R=J_nnn/J_nn) is examined by generating accurate data for large lattices at a particular value of the ratio (R=1). Our study does not support a first-order transition and a convincing finite-size scaling analysis of the model is presented, yielding accurate estimates for all critical exponents for R=1. The magnetic exponents are found to obey “weak universality” in accordance with a previous conjecture.