A New Class of Cellular Automata with a Discontinuous Glass Transition

We introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete times which allows only emptying sites. We prove that the threshold density ρ _c for convergence to a completely empty configuration is non trivial, 0<ρ _c <1, contrary to standard bootstrap percolation. Furthermore we prove that in the subcritical regime, ρ<ρ _c , emptying always occurs exponentially fast and that ρ _c coincides with the critical density for two-dimensional oriented site percolation on ℤ². This is known to occur also for some cellular automata with oriented rules for which the transition is continuous in the value of the asymptotic density and the crossover length determining finite size effects diverges as a power law when the critical density is approached from below. Instead for our model we prove that the transition is discontinuous and at the same time the crossover length diverges faster than any power law. The proofs of the discontinuity and the lower bound on the crossover length use a conjecture on the critical behaviour for oriented percolation. The latter is supported by several numerical simulations and by analytical (though non rigorous) works through renormalization techniques. Finally, we will discuss why, due to the peculiar mixed critical/first order character of this transition, the model is particularly relevant to study glassy and jamming transitions. Indeed, we will show that it leads to a dynamical glass transition for a Kinetically Constrained Spin Model. Most of the results that we present are the rigorous proofs of physical arguments developed in a joint work with D.S. Fisher.     

Variational calculations on the energy levels of graphene quantum antidots

The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p _c , and a first-order phase transition for p > p _c , where p _c  ≈ 0.25. The critical exponents for p < p _c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.     

Monte Carlo simulation of Ising model on decagonal covering structure

We study the Ising model on a two-dimensional quasilattice developed from the decagonal covering structure. The periodic boundary conditions are applied to a patch of rhombus-like covering pattern. By means of the Monte Carlo simulation and the finite-size scaling analysis the critical temperature is estimated as 2.317±0.002. Two critical exponents are obtained being 1/v=0.992±0.003 and η=0.247±0.002, which are close to the values of the two-dimensional regular lattices as well as the Penrose tilings.     

Specific heat anomalies in the quasi two-dimensional monophosphate tungsten bronzes KxP4W8O32

The monophosphate tungsten bronzes K_xP₄W₈O₃₂ (0.75<x<2) are quasi-two-dimensional conductors which show electronic transitions at a critical temperature T_c depending on the concentration of the alkali metal. The phase diagram shows a maximum at for x=1.30. We report specific heat measurements in the range 120-190 K. The thermal anomalies found at the transition temperature are larger than in conventional charge density wave materials. This corroborates that the transition is not a ‘pure’ charge density wave transition and that a structural transition dominates the instability.     

Critical behavior of long linear k-mers on honeycomb lattices

Monte Carlo (MC) simulations, finite-size scaling and theoretical analysis have been carried out to study the critical behavior of long linear particles of length k (k-mers) on honeycomb lattices. A nematic phase, characterized by a big domain of parallel k-mers, is separated from the isotropic state, by a continuous transition occurring at a finite density θ_c. Our study allowed: (1) to determine the minimum value of k (k_min), which allows the formation of the nematic phase, being k_min=11; (2) to predict the dependence of θ_c on k, being θ_c(k)∝k⁻¹; and (3) to obtain the critical exponents, which indicate that the transition belongs to the 2D three-state Potts universality class.     

Variation of electronic density in the superconducting phase transition in Nb<Subscript>3</Subscript>Al

The variation of electronic density in the superconducting phase transition in the classical superconductor Nb₃Al with critical temperature T_c=18.6 K was studied using ⁷³Ge emission Mössbauer spectroscopy. A comparison of the results obtained and the data available for the ⁶⁷Zn isotope in the lattices of high-temperature superconductors revealed a correlation between the electronic density variation at the Mössbauer probe nuclei sites and the value of T_c. This correlation is assumed to be related to the dependence of the electronic density variation on the standard correlation length.     

Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ ₁ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m ₂ ~ t ^α , α< 1, on length scales beyond ξ ₁. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.     

Mutual Composite Fermion and Composite Boson approaches to balanced and imbalanced bi-layer quantum Hall system: An electronic analogy of the Helium 4 system

We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and imbalanced Bi-layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is superior to the MCF approach in studying ground states with different kinds of broken symmetries. In the phase representation of the CB theory, we first study the Excitonic superfluid (ESF) state. The theory puts spin and charge degree freedoms in the same footing, explicitly bring out the spin-charge connection and classify all the possible excitations in a systematic way. Then in the dual density representation of the CB theory, we study possible intermediate phases as the distance increases. We propose there are two critical distances d_c1 < d_c2 and three phases as the distance increases. When 0 < d < d_c1, the system is in the ESF state which breaks the internal U(1) symmetry, when d_c1 < d < d_c2, the system is in an pseudo-spin density wave (PSDW) state which breaks the translational symmetry, there is a first-order transition at d_c1 driven by the collapsing of magneto-roton minimum at a finite wavevector in the pseudo-spin channel. When d_c2 < d < ∞, the system becomes two weakly coupled ν = 1/2 Composite Fermion Fermi Liquid (FL) state. There is also a first-order transition at d = d_c2. We construct a quantum Ginzburg Landau action to describe the transition from ESF to PSDW which break the two completely different symmetries. By using the QGL action, we explicitly show that the PSDW takes a square lattice and analyze in detail the properties of the PSDW at zero and finite temperature. We also suggest that the correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature-dependent drag consistent with the experimental data. Then we study the effects of imbalance on both ESF and PSDW. In the ESF side, the system supports continuously changing fractional charges as the imbalance changes. In the PSDW side, there are two quantum phase transitions from the commensurate excitonic solid to an incommensurate excitonic solid and then to the excitonic superfluid state. We also comment on the effects of disorders and compare our results with the previous work. The very rich and interesting phases and phase transitions in the pseudo-spin channel in the BLQH is quite similar to those in ⁴He system with the distance playing the role of the pressure. A BLQH system in a periodic potential is also discussed. The Quantum Hall state to Wigner crystal transition in single layer Quantum Hall system is studied.     

Quantum phase transition in XY spin chain with three-site interaction studied in terms of Loschmidt echo and Berry phase

By means of the Loschmidt Echo (LE) and Berry Phase (BP) calculations, quantum phase transition (QPT) of an XY spin chain with three-site interaction (α) in a transverse magnetic field (λ) is studied. Both the LE and BP?s λ derivative present anomaly behaviors at the critical regions λ₁,λ₂ and λ₃. The model is in the Ferromagnetic phase as λ>λ₁=1+α and in the Spin Liquid I phase as −1+α<λ<1+α. λ₁ and λ₂ are independent on the anisotropy parameter γ. But, the anisotropy interaction can shift the critical line λ₃ between the Spin Liquid II phase and the Ferromagnetic phase. The present work suggests that QPT of the XY spin chain with three-site interaction can be characterized by exploring the dynamical behaviors of the LE and BP.     

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M_H ≅ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L_t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.     

Kauffman Cellular Automata on Quasicrystal Topology

In this paper, we perform numerical simulations to study Kauffman cellular automata (KCA) on quasiperiod lattices. In particular, we investigate phase transition, magnetic entropy, and propagation speed of the damage on these lattices. Both the critical threshold parameter \(p_{c}\) and the critical exponents are estimated with good precision. In order to investigate the increase of statistical fluctuations and the onset of chaos in the critical region of the model, we have also defined a magnetic entropy to these systems. It is seen that the magnetic entropy behaves in a different way when one passes from the frozen regime (p < p_c) to the chaotic regime (p > p_c). For a further analysis, the robustness of the propagation of failures is checked by introducing a quenched site dilution probability q on the lattices. It is seen that the damage spreading is quite sensitive when a small fraction of the lattice sites are disconnected. A finite-size scaling analysis is employed to estimate the critical exponents. From these numerical estimates, we claim that on both pure (q =?0) and diluted (q =?0.05) quasiperiodic lattices, the KCA model belongs to the same universality class than on square lattices. Furthermore, with the aim of comparing the dynamical behavior between periodic and quasiperiodic systems, the propagation speed of the damage is also calculated for the square lattice assuming the same conditions. It is found that on square lattices the propagation speed of the damage obeys a power law as \(v\sim (p-p_{c})^{\alpha }\), whereas on quasiperiod lattices, it follows a logarithmic law as \(v \sim \ln (p-p_{c})^{\alpha }\).     

The simplified Hubbard model in one and two dimensions

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero couplingU and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function ofU, temperature and band fillingp. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at ?4d<U _c (p)≦?2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order forU>U _c . The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.     

Two-Dimensional SIR Epidemics with Long Range Infection

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law p(x)～|x|^?σ?2 for the probability that a site can infect another site a distance vector x apart. As in I we present detailed results for the critical case, for the supercritical case with σ=2, and for the supercritical case with 0<σ<2. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For σ=2 we find generic power laws with σ-dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on σ in the regime 0<σ<2, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for σ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder et al. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.     

Thermodynamic behavior of a water model with a liquid-liquid critical point

In this paper we calculate the constant pressure specific heat response of a water model with a liquid-liquid critical point. We show how, due to the existence of the critical point, there is a secondary maximum in the specific heat at some temperature T_*>T_h for any pressure P>P_c, being T_h the first order transition temperature between the high and the low density liquid phases and P_c the pressure of the critical point. This secondary maximum does not correspond to any long range correlated phase transition and does not show up in the temperature dependence of the isothermal compressibility.     

Effect of high pressure on the fluctuation paraconductivity in Y0.95Pr0.05Ba2Cu3O7−δ single crystals

The effect of high hydrostatic pressure up to 17 kbar on the fluctuation conductivity of lightly Pr-doped Y_1−xPr_xBa₂Cu₃O_7−δ (x ≈ 0.05) single crystals is investigated. We show that in contrast to non-doped YBa₂Cu₃O_7−δ samples, application of a high pressure leads to a substantial increase of the pressure derivative of the coherence length dξ_c/dP and a temperature shift of the 2D-3D crossover point. Possible mechanisms of the influence of high pressure on the critical temperature and the coherence length are discussed within the framework of a model assuming the presence of singularities in the charge carriers electron spectrum typical for lattices with strong coupling.     

Ground-state phase diagrams of Ising metamagnet in a mixed longitudinal and transverse magnetic field

The ground-state magnetic properties of a two-sublattice Ising metamagnet in a mixed longitudinal and transverse magnetic field are studied within the effective-field theory. A parameter j₂=J₂/J₁ is introduced, which reflects the strength ratio of spin coupling between adjacent planes and in each plane. In addition to the second-order transition lines, the first-order transition lines are also presented, since the ground-state energy can be calculated numerically. The ground-state phase diagrams in h_x–h_z are presented. The results show that when j₂<0 the phase transition of the system is always first-order for h_x<2.751, and when −1000?j₂<0 it is always second-order for h_x>4.36. For the given h_x (0<h_x<14.71), the longitudinal critical magnetic field increases as j₂ decreases. The reentrant phenomenon occurs in the range of j₂<−11.89, h_x>14.71. There is no fourth-order critical point in the phase diagrams given by using EFT as found by using mean field theory (MFT).     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Growth temperature dependence of the hysteretic behavior of Ni0.5Zn0.5Fe2O4 thin films

Herein, a discussion of the effect of deposition temperature on the magnetic behavior of Ni_0.5Zn_0.5Fe₂O₄ thin films. The thin films were grown by r.f. sputtering technique on (1 0 0) MgO single-crystal substrates at deposition temperatures ranging between 400 and 800 °C. The grain boundary microstructure was analyzed via atomic force microscopy (AFM). AFM images show that grain size (φ∼70-112 nm) increases with increasing deposition temperature, according to a diffusion growth model. From magneto-optical Kerr effect (MOKE) measurements at room temperature, coercive fields, H_c, between 37and 131 Oe were measured. The coercive field, H_c, as a function of grain size, reaches a maximum value of 131 Oe for φ ∼93 nm, while the relative saturation magnetization exhibits a minimum value at this grain size. The behaviors observed were interpreted as the existence of a critical size for the transition from single- to multi-domain regime. The saturation magnetization (21 emu/g<M_s<60 emu/g) was employed to quantify the critical magnetic intergranular correlation length (L_c≈166 nm), where a single-grain to coupled-grain behavior transition occurs. Experimental hysteresis loops were fitted by the Jiles-Atherton model (JAM). The value of the k-parameter of the JAM fitted by means of this model (k/μ_o∼50 A m²) was correlated to the domain size from the behavior of k, we observed a maximum in the density of defects for the sample with φ∼93 nm.     

Robust thermal quantum correlation and quantum phase transition of spin system on fractal lattices

We investigate the quantum correlation measured by quantum discord (QD) for thermalized ferromagnetic Heisenberg spin systems in one-dimensional chains and on fractal lattices using the decimation renormalization group approach. It is found that the QD between two non-nearest-neighbor end spins exhibits some interesting behaviors which depend on the anisotropic parameter Δ, the temperature T, and the size of system L. With increasing Δ continuously, the QD possesses a cuspate change at Δ = 0 which is a critical point of quantum phase transition (QPT). There presents the “regrowth” tendency of QD with increasing T at Δ < 0, in contrast to the “growth” of QD at Δ > 0. As the size of the system L becomes large, there still exists considerable thermal QD between long-distance end sites in spin chains and on the fractal lattices even at unentangled states, and the long-distance QD can spotlight the presence of QPT. The robustness of QD on the diamond-type hierarchical lattices is stronger than that in spin chains and Koch curves, which indicates that the fractal can affect the behaviors of quantum correlation.     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998