Quantum Ising spin-glass

A random, quantum model of interacting spins, where the spin operators are represented by bilinear combinations of fermions, is studied in the Ising limit and in the static approximation. Assuming replica symmetry we recover basically the results of Sherrington and Kirkpatrick. Effects of quantum fluctuations remain in the determination of the static susceptibility χ as an independent order parameter and the breakdown of the Fischer relation.     

Exactly solvable model exhibiting a multicritical point

A hypercubic d-dimensional lattice of spins with nearest neighbor ferromagnetic coupling and next nearest neighbor antiferromagnetic coupling along a single axis is studied in the spherical model limit (n→∞) and is found to exhibit a multicritical point of the uniaxial Lifshitz type. The shape of the λ line is calculated explicitly in the vicinity of the multicritical point, and analytic expressions are given for the shift exponent ψ(d) and its amplitudes A_±(d). The amplitude A_(d) changes sign for d = 3.     

Nematic-smectic-A-smectic-C multicritical point: An alternative model

A new Landau-type phenomenological free-energy function to describe the nematic-smectic-A transition, smectic-A-smectic-C transition and nematic-smectic-C transition is proposed. The influence of pressure on the these phase transitions is discussed by varying the coupling between various order parameters. The phase diagram of the thermodynamic parameters is studied and a possible nematic-smectic-A-smectic-C bicritical point is predicted. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a bicritical point is observed in the phase diagram. The obtained topology of the pressure-temperature phase diagram is consistent with experimental results.     

On the p-spin interaction transverse Ising spin-glass model without replicas

The p-spin interaction Ising spin glass model in the presence of a transverse field is studied in the large p-limit by means of a convenient operator extension of the cavity fields method avoiding replicas and the Trotter-Suzuki transformation. The results appear quite consistent with those recently obtained for the same model using conventional treatments within the replica trick. This gives additional support to the cavity fields approach as a promising tool towards a general theory of classical and quantum spin glasses.     

Calculation of wave vector dependent susceptibility for an Ising spin-glass

In an attempt to understand Murani's neutron scattering results from the spin glass AuFe, we have calculated the wavevector dependent susceptibility χ(q), using the approach pioneered by Edwards and Anderson. We find that Edwards Anderson type of approach fails to account for the neutron scattering data.     

Critical behavior and coexistence near a superconducting-ferromagnetic multicritical point

It is shown that in the vicinity of the multicritical transition point of a ferromagnetic cuperconductor a) critical fluctuations of the superconducting order parameter should become observable in 3 dimensions, b) for planar magnetic ordering magnetism and superconductivity should coexist.     

A renormalization-group study of an Ising spin-glass with annealed vacancies

Systems driven and characterized by fluctuations in density and magnetization can be realistically modeled using the Blume–Emery–Griffiths model; a spin-1 Ising model with bilinear, biquadratic, and crystal-field interactions. In this study, renormalization-group techniques are used on an exactly solvable system in which frustration is present due to competing ferromagnetic and antiferromagnetic interactions. Thus, this calculation models a spin-glass system with annealed vacancies. To determine the effects of these competing bilinear interactions, an exactly solvable frustrated hierarchical model has been constructed, similar to those introduced to study spin glasses [S.R. McKay, A.N. Berker, S. Kirkpatrick, Phys. Rev. Lett. 48 (1982) 767]. Phase diagrams have been calculated for a series of planes of constant biquadratic coupling while varying the temperature and concentration of annealed vacancies in the system. In addition, a phase diagram was produced for constant concentration of annealed vacancies as the biquadratic coupling (i.e. clustering bias) was varied. Each phase diagram reveals three qualitatively unique basins of attraction, each corresponding to a phase distinguished by a unique renormalization-group trajectory. The sink of each trajectory is interpreted to determine the nature of each phase: dense paramagnetic, dilute paramagnetic and spin-glass.     

On the type of multicritical point in NH4Cl

The temperature dependence of the tensor component d₁₄ of the nonlinear quadratic susceptibility, measured at atmospheric pressure across the order-disorder phase transition in NH₄Cl, was fitted to different expressions derived from the classical Landau theory for discontinuous phase transitions. These expressions correspond to multicritical points of different type. Best fits are obtained with the assumption of a tetracritical point or a pentacritical point for NH₄Cl.