Sub-aging in a domain growth model

We study analytically the aging dynamics of the O(n) model in the limit of , with conserved and with non-conserved order parameter. While in the non-conserved dynamics, the autocorrelation function scales in the usual way , in the case of a conserved order parameter, `multiscaling' manifests itself in the form , with a relaxation time growing more slowly than the age of the system (sub-aging), and h(t) a function growing faster than any length scale of the problem. In both cases, the effective temperature associated to the violation of the fluctuation theorem tends to infinity in the asymptotic limit of large waiting times. Received 15 May 2000 and Received in final form 5 July 2000     

Multiscaling and multifractality in an one-dimensional Ising model

Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular energy levels display multiscaling with the scaling length ℓ = 1/M _n, where n denotes the number of spins and M_n is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal properties. Received 10 July 2000 and Received in final form 6 November 2000     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece [2,3] which show that two of these parameters, G and G _c, take universal values in the . In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume limit. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for T _c and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at. Received 20 September 2000 and Received in final form 10 January 2001     

The statistical mechanics of turbo codes

The “turbo codes”, recently proposed by Berrou et al. [1] are written as a disordered spin Hamiltonian. It is shown that there exists a threshold such that for signal to noise ratios the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitely long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations. Received 14 March 2000 and Received in final form 17 July 2000     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

Interactions of several replicas in the random field Ising model

The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the n = 0 limit allows one to discuss the renormalization group properties in spite of this phenomenon. The attraction of pairs of replicas is enhanced under renormalization flow and no stable fixed point is found. Consequently, an instability occurs in the paramagnetic region, before one reaches the Curie line, signalling the onset of replica symmetry breaking. Received 28 July 2000     

Design study of 3-D tomography diagnostics for spherical tokamaks

A novel three-dimensional (3-D) tomography software has been developed for spherical tokamak (ST) plasmas with thin central coils. It enables us to measure whole 3-D annular profiles of ST plasma emissivity (line spectrum etc.) using limited number of detectors located on a sphere outside of its separatrix. The numbers and positions of detectors have been optimized for STs that contain low-n toroidal modes from n = 1 to 5. Mathematical method allowing for the removal of the thin central coil from the region of reconstruction and to reconstruct STs with single and double axes are also discussed. The shadow effect of center coil region was found to limit the reconstruction accuracy, indicating that the low-aspect ratio torus (ST) is essential to this new 3-D tomography diagnostics. Received 17 August 2000 and Received in final form 16 November 2000     

Magnetic relaxation phenomena in a CuMn spin glass

Experiments on the temperature and time dependence of the response function and the field cooled magnetisation of a Cu(Mn) spin glass at temperatures below the zero field spin glass temperature are used to explore the non-equilibrium nature of the underlying spin configuration. The results imply that a certain spin configuration is imprinted on the system as the temperature is decreased at a constant cooling rate. The cooling rate governs the magnitude of the FC magnetisation ((H,T)). Any intermittent halt at a constant temperature, , imprints an extended spin configuration, a process that is reflected e.g. in a downward relaxation of . On continued cooling at the same rate, the magnitude of (T) remains at a lower level than that of a continuous cooling curve. These results are put into the context of the corresponding behaviour of the response function as observed in measurements of the relaxation of the zero field cooled magnetisation. Received 27 October 1998 and Received in final form 30 November 1998     

Large-n limit of the Heisenberg model: Random external field and random uniaxial anisotropy

The thermodynamic equivalence of the large-n limit of then-vector model in a random external field and the corresponding disordered spherical model is proved. An analytic expression for the free energy and a phase diagram of the large-n limit of then-vector model with random uniaxial anisotropy are obtained by rigorous argument. The ferromagnetic order in the large-n limit is proved to be stable against the switching on of an arbitrarily small random anisotropy.     

The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

The renormalisation group approach is applied to the study of the short-time critical behaviour of the d-dimensional Ginzburg-Landau model with long-range interaction of the form in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents and of the order parameter and the response function respectively, are calculated to the second order in . Received 9 June 2000 and Received in final form 2 August 2000     

Simple stochastic models showing strong anomalous diffusion

We show that strong anomalous diffusion, i.e. where is a nonlinear function of q, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function cannot hold, a part (sometimes) in the limit of very small , now . Moreover the comparison with previous numerical results shows that the shape of is not universal, i.e., one can have systems with the same but different F. Received 14 April 2000     

Studies of the exactly dimerized bilayer Heisenberg model via strong coupling expansions

The one-triplet excitation spectra and thermodynamic properties for the dimerized phase of the frustrated bilayer Heisenberg model are studied using strong-coupling expansion theory. The model has an exact dimerized ground state as well as exact one-triplet excitations in a special case that the frustration J₂ is equal to the in-plane coupling J₁. We demonstrate that the models with and without frustrations have distinct excitation spectra, so their thermodynamic properties exhibit quite different behaviors. Especially, the low-temperature behaviors of the frustrated model with J ₁=J ₂ are independent of the inter-dimer couplings, due to the exact one-triplet excitations. Received 16 March 2000 and Received in final form 2 July 2000     

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed. Received 22 August 2000     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S=1/2 spin. So far, the semi-classical case, where each spin reduces to a plane rotator, has been considered extensively. We found that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically. Received 20 February 2000     

Fragmentation of water clusters: Molecular-dynamics simulation study

The fragmentation of water clusters, [(H ₂ O)_n;n = 2-8], have been investigated by using molecular-dynamics simulation method. In the simulations a polarizable-dissociable potential energy function for water has been used. Particular attention has bee paid to investigate the effect of structural properties and cluster size on the fragmentation. Received 27 April 2000 and Received in final form 6 October 2000     

Stretched exponential relaxation on the hypercube and the glass transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of the relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential over several orders of magnitude in q(t). As the critical dilution for percolation is approached, the time constant tends to diverge and the stretching exponent drops towards 1/3. As the same pattern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition may be pictured as a percolation transition in phase space. Received 16 June 2000 and Received in final form 13 October 2000     

Spin-wave excitations in finite chain segments of the diluted one-dimensional Heisenberg antiferromagnet CsM{n_{1 - x}}M{g_x}B{r_3}

The inelastic neutron scattering technique was employed to study the magnetic excitation spectra in the diluted one-dimensional Heisenberg antiferromagnet CsMn_1-xMg_xBr₃ (x =0, 0.05, 0.10, 0.25, 0.50). The spectral response is interpreted in terms of spin-wave excitations in finite chain segments of Mn²⁺ ions, which are found to exist as long as the chain length exceeds twice the wavelength of the spin excitation. This limit determines the crossover into the mesoscopic regime. Received 31 December 1999