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p. 3083-3089 Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-07-24T16:46:14Z No. of bitstreams: 1 1111111aa.pdf: 127597 bytes, checksum: a869ca4122bbe5dbe5975e1c71c77179 (MD5) Approved for entry into archive by Rodrigo Meirelles (rodrigomei@ufba.br) on 2013-11-16T11:58:33Z (GMT) No. of bitstreams: 1 1111111aa.pdf: 127597 bytes, checksum: a869ca4122bbe5dbe5975e1c71c77179 (MD5) Made available in DSpace on 2013-11-16T11:58:33Z (GMT). No. of bitstreams: 1 1111111aa.pdf: 127597 bytes, checksum: a869ca4122bbe5dbe5975e1c71c77179 (MD5) Previous issue date: 2000 The model of Blume-Capel on the Sierpinski gasket is investigated within the method of transfer matrices, where the thermodynamic functions are obtained after the numerical iteration of a set of discrete maps. The analysis of the T50 transition shows that, for antiferromagnetic coupling and a finite interval of self-energy coefficient, the correlation length diverges as exp(Jef f /T), with superimposed log-periodic oscillations in terms of the reduced temperature t5exp(2uJef fu/T). Both the period of oscillations and the effective interaction Je f f depend on the strength of the actual coupling constants. In the antiferromagnetic regime, residual entropy is found for three different values of the self-energy parameter. The variation of this parameter leads, in the case of ferromagnetic coupling, to a more complex behavior for the correlation length than the already known exp@exp(Jef f /T)# dependence observed for the Ising and Potts models. Salvador

p. 3083-3089 Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-07-24T16:46:14Z No. of bitstreams: 1 1111111aa.pdf: 127597 bytes, checksum: a869ca4122bbe5dbe5975e1c71c77179 (MD5) Approved for entry into archive by Rodrigo Meirelles (rodrigomei@ufba.br) on 2013-11-16T11:58:33Z (GMT) No. of bitstreams: 1 1111111aa.pdf: 127597 bytes, checksum: a869ca4122bbe5dbe5975e1c71c77179 (MD5) Made available in DSpace on 2013-11-16T11:58:33Z (GMT). No. of bitstreams: 1 1111111aa.pdf: 127597 bytes, checksum: a869ca4122bbe5dbe5975e1c71c77179 (MD5) Previous issue date: 2000 The model of Blume-Capel on the Sierpinski gasket is investigated within the method of transfer matrices, where the thermodynamic functions are obtained after the numerical iteration of a set of discrete maps. The analysis of the T50 transition shows that, for antiferromagnetic coupling and a finite interval of self-energy coefficient, the correlation length diverges as exp(Jef f /T), with superimposed log-periodic oscillations in terms of the reduced temperature t5exp(2uJef fu/T). Both the period of oscillations and the effective interaction Je f f depend on the strength of the actual coupling constants. In the antiferromagnetic regime, residual entropy is found for three different values of the self-energy parameter. The variation of this parameter leads, in the case of ferromagnetic coupling, to a more complex behavior for the correlation length than the already known exp@exp(Jef f /T)# dependence observed for the Ising and Potts models. Salvador

p. 7196-7199 Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-07-24T20:27:12Z No. of bitstreams: 1 9999999999999999999.pdf: 95864 bytes, checksum: f78331d293d85e4570e90deb8fce3893 (MD5) Approved for entry into archive by Rodrigo Meirelles (rodrigomei@ufba.br) on 2013-11-19T20:21:05Z (GMT) No. of bitstreams: 1 9999999999999999999.pdf: 95864 bytes, checksum: f78331d293d85e4570e90deb8fce3893 (MD5) Made available in DSpace on 2013-11-19T20:21:05Z (GMT). No. of bitstreams: 1 9999999999999999999.pdf: 95864 bytes, checksum: f78331d293d85e4570e90deb8fce3893 (MD5) Previous issue date: 2000 This work analyzes the behavior of Ising spins on a hierarchical lattice subject to relevant fluctuations on the coupling constants induced by a deterministic aperiodic sequence. The thermodynamical functions are evaluated within the method of transfer matrices. It is shown that log-periodic oscillations in the reduced temperature are present for all thermodynamical functions close to the critical point and that the nature of oscillations changes discontinuously at Tc : for T.Tc they are almost pure sinusoidal, while, for T,Tc , a second harmonic to the fundamental frequency is clearly observed. Salvador

p. 150-157 Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-08-01T18:54:15Z No. of bitstreams: 1 33333333333333333.pdf: 163675 bytes, checksum: 9c9c27253138c5b905e067b1dd1ae3ba (MD5) Approved for entry into archive by Vilma Conceição(vilmagc@ufba.br) on 2013-08-05T17:53:45Z (GMT) No. of bitstreams: 1 33333333333333333.pdf: 163675 bytes, checksum: 9c9c27253138c5b905e067b1dd1ae3ba (MD5) Made available in DSpace on 2013-08-05T17:53:45Z (GMT). No. of bitstreams: 1 33333333333333333.pdf: 163675 bytes, checksum: 9c9c27253138c5b905e067b1dd1ae3ba (MD5) Previous issue date: 1999 This work brings an analysis of the behavior of Ising spins on a hierarchical lattice subject to relevant fluctuations on the coupling constants that are induced by a deterministic aperiodic sequence. The thermodynamical functions are evaluated after the numerical iteration of a set of coupled maps, obtained within the method of transfer matrices. The typical specific heat cusp of the homogeneous system is destroyed by the fluctuations, which also cause changes in the values of all critical exponents. Salvador

p. 150-157 Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-08-01T18:54:15Z No. of bitstreams: 1 33333333333333333.pdf: 163675 bytes, checksum: 9c9c27253138c5b905e067b1dd1ae3ba (MD5) Approved for entry into archive by Vilma Conceição(vilmagc@ufba.br) on 2013-08-05T17:53:45Z (GMT) No. of bitstreams: 1 33333333333333333.pdf: 163675 bytes, checksum: 9c9c27253138c5b905e067b1dd1ae3ba (MD5) Made available in DSpace on 2013-08-05T17:53:45Z (GMT). No. of bitstreams: 1 33333333333333333.pdf: 163675 bytes, checksum: 9c9c27253138c5b905e067b1dd1ae3ba (MD5) Previous issue date: 1999 This work brings an analysis of the behavior of Ising spins on a hierarchical lattice subject to relevant fluctuations on the coupling constants that are induced by a deterministic aperiodic sequence. The thermodynamical functions are evaluated after the numerical iteration of a set of coupled maps, obtained within the method of transfer matrices. The typical specific heat cusp of the homogeneous system is destroyed by the fluctuations, which also cause changes in the values of all critical exponents. Salvador

p. 1429-1436 Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-08-26T12:55:23Z No. of bitstreams: 1 111111111w.pdf: 180369 bytes, checksum: 0c86c5d2f9e11e2d16bca8619f8b3698 (MD5) Approved for entry into archive by Rodrigo Meirelles(rodrigomei@ufba.br) on 2013-10-09T19:44:43Z (GMT) No. of bitstreams: 1 111111111w.pdf: 180369 bytes, checksum: 0c86c5d2f9e11e2d16bca8619f8b3698 (MD5) Made available in DSpace on 2013-10-09T19:44:43Z (GMT). No. of bitstreams: 1 111111111w.pdf: 180369 bytes, checksum: 0c86c5d2f9e11e2d16bca8619f8b3698 (MD5) Previous issue date: 1997 We include extra aperiodic interactions in the Ising model with competing ferromagnetic and antiferromagnetic interactions between first and second neighbors along the branches of a Cayley tree. The problem is formulated as a nonlinear map whose attractors correspond to solutions deep in the interior of the tree. We present some analytical and numerical calculations for aperiodic interactions introduced according to the rules of a Koch curve and a Fibonacci sequence. For small values of a parameter of aperiodicity, there are no relevant changes in the phase diagram, except for the appearance of some bumps along the paramagneticmodulated transition. As the aperiodic interactions become more important, there are several new phenomena, such as phase locking and phase splitting, and the enhancement of the regions of chaotic attractors and of co-stability of different structures. @S1063-651X~97!14307-0# Salvador