F. C. Sá Barreto

New effective field theory for the transverse Ising model

Abstract A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.

Renormalization group studies of the Ashkin-Teller model

The two-and-three-dimensional Ashkin-Teller model is studied within two renormalization group treatments. The complete flow diagram is obtained for this two-parameter Hamiltonian and the results for the critical couplings and critical exponents are compared to the exact ones when avaible.

Ferroelectric and antiferroelectric dynamics of pseudo‐one‐dimensional CsD2PO4

A simple model is proposed for the pseudo‐one‐dimensional (1d) ferroelectric and antiferroelectric phase transitions in CsD2PO4 which is based on the behavior of spin 1/2 Ising chains in a longitudinal molecular field. The observed phase diagram can be reproduced if one assumes that the coupling constant beween ’’unlike’’ chains changes its sign when the hydrostatic pressure exceeds a critical value. In addition to the usual ’’critical’’ slowing down of the order parameter fluctuations an ’’anisotropy’’ slowing down is predicted which may explain the fact that the soft modes in 1d CsH2PO4 and PbHPO4 are much slower than in 3d KH2PO4 and KD2PO4.

Upper bounds on the critical temperature for the two-dimensional Blume-Emery-Griffiths model

We obtain rigorous upper bounds for the critical temperature associated with second-order phase transitions of the two-dimensional spin-1 BEG model for real values ofK andD coupling constants and forJ≥0. We use some correlation equalities and inequalities to show the exponential decay of the two-point function characterizing the disordered phase.

Dynamical behavior of the random-bond transverse Ising model with four-spin interactions

We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. We analyze how the presence of disorder affect the dynamical behavior of the system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced. Such crossover is also present in the case of an increase in bond dilution. The role of time evolution of one-dimensional quantum spin systems has been a long-standing theoretical and experimental problem. 1 Among them, the transverse Ising model with multispin interactions, regarded as one of the simplest with a nontrivial dynamics, has attracted considerable interest in recent years. 2,3 On the other hand, the presence of bond randomness has been shown to affect the behavior of magnetic materials in a drastic way providing a very rich area of investigation. In some materials it is present in the form of dilution caused by missing magnetic bonds or sites. In other class of systems it manifests itself through fluctuations in the magnitude of the exchange couplings due to structural disorder, as in glassy materials. Most of the research in disordered systems have been concentrated on obtaining phase diagrams and thermodynamic functions. 3 Much less effort has been made to obtain the dynamical behavior of these systems. Recently, the time evolution of the usual two-body random transverse Ising system was carried out by means of the method of recurrence relations. 4 The crossover from a central

Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume–Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature. The obtained results improve over effective field type results.

Chaotic Bohm's trajectories in a quantum circular billiard

Abstract We use Bohms quantum mechanics to study the dynamics of a particle trapped in a circular billiard. The trajectories can be either regular or chaotic, depending on the initial wave packet. The system undergoes a transition from regular to chaotic behavior as the amplitude of a component of the wave packet is increased.

Dynamical behavior of the four-body transverse Ising model with random bonds and fields

We study the effect of random bonds and fields on the dynamical behavior of the one-dimensional transverse Ising model with four-spin interactions. We consider finite chains of increasing size to determine the time-dependent correlation function and the longitudinal relaxation function of the infinite chain. In this fully disordered system we observe a crossover from a collective modetype of dynamics to that of a central regime.

Ferrroelectric phase transitions and the Ising model

The Ising model has been an important theoretical tool in the understanding of phase transitions in ferroelectric materials. We first review how it relates to the underlying physics of order-disorder phase transitions in these systems, as well as mean-field results for the spontaneous polarization and the dielectric constant near the critical temperature. For hydrogen-bonded ferroelectrics, a term of interaction with an external transverse field is necessary to account for proton tunneling between the two minima of a double-well potential. Finally, we discuss both experimental and theoretical results for the problems of proton-lattice interactions, central peak dynamics, dynamical behavior of pseudo-one-dimensional ferroelectrics and pressure effects on hydrogen bonded ferroelectrics.

Some Upper Bounds for the Critical Temperature for Ising Model with Four-spin Interactions

Upper bounds for the critical temperature of Ising models with different types of four-spin interactions on honeycomb and square lattices, which act only between the nearest-neighbor sites or to the nearest- and next-nearest-neighbor sites in addition to the conventional pair interactions, are obtained, using an exact relation for the two-spin correlation functions and rigorous inequalities for the spin correlation functions.