Amnon Aharony

Magnetically driven ferroelectric order in Ni3V2O8

We show that long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition in Ni3V2O8. The temperature and magnetic-field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry using Landau theory for continuous phase transitions, which shows that the spin structure alone can break spatial inversion symmetry leading to ferroelectric order. This phenomenological theory explains our experimental observation that the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter.

Random field effects in disordered anisotropic antiferromagnets

A uniform magnetic field is shown to generate random local fields in uniaxially anisotropic antiferromagnets with random exchange interactions. This leads to a stronger divergence of the temperature derivative of the static susceptibility even at zero field, and to a drastic change in the critical exponents at the Ising-like antiferromagnetic transition as well as at the tricritical or bicritical points occurring at finite fields.

Anomalous Diffusion on Percolating Clusters

Much of the recent renewed interest in percolation theory is related to the realization that percolation clusters are self-similar,1 and may thus be modeled by fractal structures.2 On a fractal structure, all the physical properties behave as powers of the relevant length scale, L. This behavior crosses over to a homogeneous one (i.e. independent of L, for appropriately defined quantities), on length scales larger than the percolation connectedness (or correlation) length, ξ∝|p−pc|−v. Assuming that ξ is the only important length in the problem, all other lengths should be measured in units of ξ, and thus depend on L only via the ratio L/ξ. This implies scaling. For example, above the percolation threshold (p≥pc) one has1

PATH-CROSSING EXPONENTS AND THE EXTERNAL PERIMETER IN 2D PERCOLATION

M\left( L \right) = {L^D}m\left( {L/\zeta } \right)

Competing magnetic phases on a kagomé staircase

(1) for the number of sites on the infinite incipient cluster within a volume of linear size L. The exponent D is the fractal dimensionality 2 of the cluster in the self-similar regime, and the scaling function m(x) behaves as a constant for x→0 and as m(x)∿xβ/v for x»1, so that M(L)∿LdP∞. Here, d is the Euclidean dimensionality of space, and P∞ ∿ ξ−β/v ∿ (p−pc)β is the probability per site to belong to the infinite cluster. Thus, one identifies D=d−β/v.

Magnetic frustration model for superconductivity in planar CuO2 systems

For pt.II see ibid. vol.17, p.435 (1984). In the first two papers of this series the authors considered self-similar fractal lattices with a finite order of ramification R. In the present paper they study physical models defined on a family of fractals with R= infinity . In order to characterise the geometry of these systems, they need the connectivity Q and the lacunarity L, in addition to the fractal dimensionality D. It is found that discrete-symmetry spin models on these lattices undergo a phase transition at Tc>0. An approximate renormalisation group scheme is constructed and used to find the dependence of Tc and the critical exponents on the geometrical factors. They also solve the problem of resistor networks on these fractals, and discuss its consequences concerning spin models with continuous symmetry.

Self similarity and correlations in percolation

2D Percolation path exponents

Absence of ferromagnetic long range order in random isotropic dipolar magnets and in similar systems

x^{\cal P}_{\ell}