Uniform uniaxial anisotropic systems with coupled vector order parameters

Phase transitions in magnets, described by two coupled, m-component vector order parameters, having uniform uniaxial anisotropies are studied. Using a phenomenological model, it is shown that when both order parameters are anisotropic, phase transitions are always second order, in either the uniaxial or the (m???1)-isotropic phase. This is contrary to the isotropic case of two coupled order parameters, for which phase transitions are fluctuation-induced first order. The transitions are still continuous into the m-isotropic phase even when the only anisotropic order parameter is the one with the lowest mean-field critical temperature. New discontinuous transitions still occur in either the uniaxial or the (m???1)-isotropic phase, when the only anisotropic order parameter has the highest mean-field critical temperature.     

Phase transitions with several order parameters

The predictions of catastrophe theory for phase transitions involving more than one order parameter are given. These predictions are compared with those of other theories. For the simplest transition involving two order parameters it is found that there is a parameter which does not affect the topology of the phase diagram, which does affect certain angles in the diagram, and whose measured value will not depend on the scale of external physical variables. Comparison with renormalization theory predictions for this parameter leads to general observations on the relation of catastrophe theory and renormalization theory.     

Phase transitions in anisotropic magnetic superlattices

The paper reports a theoretical study of phase transitions in antiferromagnetic superlattices. The boundaries of stability of the ferro-and antiferromagnetic phases have been calculated by a model taking into account the layered structure of these materials. The expressions obtained are precise in the limit of a large number of layers. In the case of a small number of layers, the problem reduces to a simple numerical procedure of solving a transcendental equation. The critical field is shown to depend substantially on the biquadratic non-Heisenberg exchange constant. Fiz. Tverd. Tela (St. Petersburg) 39, 178–180 (January 1997)     

Phase transitions in anisotropic lattice spin systems

A general method for proving the existence of phase transitions is presented and applied to six nearest neighbor models, both classical and quantum mechanical, on the two dimensional square lattice. Included are some two dimensional Heisenberg models. All models are anisotropic in the sense that the groundstate is only finitely degenerate. Using our method which combines a Peierls argument with reflection positivity, i.e. chessboard estimates, and the principle of exponential localization we show that five of them have long range order at sufficiently low temperature. A possible exception is the quantum mechanical, anisotropic Heisenberg ferromagnet for which reflection positivity isnot proved, but for which the rest of the proof is valid.Work partially supported by U.S. National Science Foundation grant no. MPS 75-11864Work partially supported by U.S. National Science Foundation grant no. MCS 75-21684 A01     

Disordered magnetic phases and magnetic transitions in non anisotropic frustrated systems

Numerous studies have been devoted to disordered magnetic phases which show the existence of several types of disorder in non-anisotropic systems. Semi-disordered systems which retain at least partially long-range order (reentrant properties and randomly canted structures) and fully disordered systems (spin cluster and soft transition systems, true spin glass state) are shortly reviewed. Several characteristic experiments and results are presented and commented on, such as alternative, nonlinear and static susceptibilities, thermoremanence, ageing effects, neutron diffraction and Mössbauer spectroscopy. The possible types of disordered magnetic phases are discussed as a function of a sharp (or soft) transition and of a more or less fast dynamics. In true spin glasses, some problems are still open while in the other disordered phases the unresolved questions are numerous.     

Phase transitions in anisotropic classical Heisenberg ferromagnets

The method of Peierls is used to prove the existence of a spontaneous magnetization for a spin system with nearest-neighbor interactions and Hamiltonian a (classical) unit vector at thei'th site, with ||<0.0298 and 0.0198 for a square lattice and simple cubic lattice, respectively.Research supported by the National Science Foundation Grant No. GP 11454.     

Phase transitions in hybrid SFS structures with thin superconducting layers

Features of a phase transition between 0 and π states in superconductor/ferromagnet/superconductor (SFS) Josephson structures with thin superconducting layers and a ferromagnetic barrier are studied experimentally and theoretically. The dependence of the critical temperature T_c of a transition of the hybrid structure to a superconducting state on the thickness of superconducting layers d_s is analyzed by a local method involving measurements of the nonlinear microwave response of the system by a near-field probe. An anomalous increase in the measured temperature T_c at the reduction of the thickness d_s is detected and is attributed to the 0-π transition.     

Phase transitions in hybrid SFS structures with thin superconducting layers

Calculations of critical temperature T _c of the phase transition to superconducting state of a superconductor/ ferromagnet/superconductor (SFS) hybrid structure with proximity effect is performed on the base of linearized Usadel equations. It is shown that the proximity effect between S and F metals and the exchange interaction can induce an inhomogeneous superconducting state with longitudinal to layers Δ _∝ exp(ipz) modulation of the superconductivity order parameter, which is characterized by nonzero value of the wave number p, describing the Larkin–Ovchinnikov–Fulde–Ferrell instability. Influence of this instability on transitions between 0- and π-states of the SFS structure is studied. It is shown that the 0–π transition is accompanied by a nonmonotonic dependence of both the critical temperature T _c and the effective penetration depth Λ of the magnetic field into the hybrid structure on the characteristic size of the ferromagnetic region.     

Phase transitions in classical vector models

The equation of state obtained earlier /6/ for 3-dimensional Ising ferromagnets in the first order in$\text{1}\text{z}$ (z is the number of the nearest neighbours) is generalized with regard to the classical D-component vector model. The results obtained are valid in a wide temperature range |τ|?[z²(D+2)]^?1 (τ=(T_c-T)/T_c) and become exact in the limit D → ∞.     

The Topological Nonconnectivity Threshold and magnetic phase transitions in classical anisotropic long-range interacting spin systems

We review, with emphasis on the dynamical point of view, the classical characteristics of the Topological Nonconnectivity Threshold (TNT), recently introduced in F. Borgonovi, G.L. Celardo, M. Maianti and E. Pedersoli, J. Stat. Phys. 116, 1435 (2004). This shows interesting connections among Topology, Dynamics, and Thermo-Statistics of ferro/paramagnetic phase transition in classical spin systems, due to the combined effect of anisotropy and long-range interactions.     

Phase transitions in experimental systems

Scaling functions of the support and of the measure have been used to characterize the scaling behavior of a dynamical system. While scaling functions for the scaling of the measure, ƒ(), have been calculated for a number of experimental systems, examples of scaling functions φ(λ) for the scaling of the support are difficult to obtain. In this contribution, we report on a phase-transition-like effect of an experimental p-doped germanium semiconductor sample. It is found that the results obtained from the dynamical scaling function agree with those obtained by Horita et al. from model maps, indicating that scaling functions for the scaling of the support are a powerful method of characterizing experimental dynamical systems.     

Symmetric Hubbard systems with superconducting magnetic response

In purely repulsive, C _4v -symmetric Hubbard clusters a correlation effect produces an effective two-body attraction and pairing; the key ingredient is the availability of W=0 pairs, that is, two-body solutions of appropriate symmetry. We study the tunneling of bound pairs in rings of 5-site units connected by weak intercell links; each unit has the topology of a CuO₄ cluster and a repulsive interaction is included on every site. Further, we test the superconducting nature of the response of this model to a threading magnetic field. We present a detailed numerical study of the two-unit ring filled with 6 particles and the three-unit ring with 8 particles; in both cases a lower filling yields normal behavior. In previous studies on 1d Hubbard chains, level crossings were reported (half-integer or fractional Aharonov-Bohm effect) which however cannot be due to superconducting pairs. In contrast, the nontrivial basis of clusters carrying W=0 pairs leads to genuine Superconducting Flux Quantization (SFQ). The data are understood in terms of a cell-perturbation theory scheme which is very accurate for weak links. This low-energy approach leads to an effective hard core boson Hamiltonian which naturally describes itinerant pairs and SFQ in mesoscopic rings. For the numerical calculations, we take advantage of a recently proposed exact diagonalization technique which can be generally applied to many-fermion problems and drastically reduces the size of the matrices to be handled.Received: 14 July 2003, Published online: 9 September 2003PACS: 71.27.+a Strongly correlated electron systems; heavy fermions - 74.20.Mn Nonconventional mechanisms - 73.22.-f Electronic structure of nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals