abstract
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 < 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 < 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 < 1.0 in the form alpha(q)=(10q(2)-33q+23)/20, beta(q)=(2q-1)/8, and gamma(q)=(q(2)-q+7)/4. On the other hand, the critical exponent nu does not depend on q. This suggests a violation of the scaling relations 2 beta+gamma=d nu and alpha+2 beta+gamma=2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.
keywords
LONG-RANGE INTERACTIONS; TSALLIS STATISTICS; MAGNETIC SYSTEMS; THERMOSTATISTICS; TEMPERATURE; SIMULATION; SCENARIO; PHASE; RELAXATION; MANGANITES
subject category
Physics
authors
Crokidakis, N; Soares-Pinto, DO; Reis, MS; Souza, AM; Sarthour, RS; Oliveira, IS
Groups
acknowledgements
The authors acknowledge S. M. D. Queiros for his comments. We would like to thanks the Brazilian funding agencies CNPq, CAPES, and the Brazilian Millennium Institute for Quantum Information for the financial supports. D.O.S.P. thanks FAPESP for financial support, M. S. R. thanks the financial support from PCI-CBPF program and A. M. S. would like to thanks the Ontario Goverment.