Finite-size analysis of a two-dimensional Ising model within a nonextensive approach.
In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic two-dimensional Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for q< or =0.5 . However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the 0.5<q< or =1.0 regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents alpha , beta , and gamma depend on the entropic index q in the range 0.5<q< or =1.0 in the form alpha(q)=(10q2-33q+23)/20 , beta(q)=(2q-1)/8 , and gamma(q)=(q2-q+7)/4 . On the other hand, the critical exponent nu does not depend on q . This suggests a violation of the scaling relations 2beta+gamma=dnu and alpha+2beta+gamma=2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.
Crokidakis
N
N
Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-340 Niterói, RJ, Brazil. nuno@if.uff.br
Soares-Pinto
D O
DO
Reis
M S
MS
Souza
A M
AM
Sarthour
R S
RS
Oliveira
I S
IS
D003198:Computer Simulation; D004574:Electromagnetic Fields; D008956:Models, Chemical; D015233:Models, Statistical; D044367:Phase Transition