Magnets with random uniaxial anisotropy: Thermodynamic properties in the large-N limit

We show that the random-axis model lends itself to a systematic large-N calculation. The model shows different behavior below and above four dimensions. The equation of state is derived and discussed in terms of “Arrott” plots. Higher-order terms in the disorder, when summed, have a crucial effect on the susceptibility which is found to be finite below four dimensions (and above four dimensions for strong disorder). A spin-glass to paramagnetic phase transition is characterized by the vanishing of the Edwards-Anderson order parameter, which differs from zero in the spin-glass phase. A cusp in the specific-heat and susceptibility is seen across the transition. The cross-over exponent and other exponents of interest are calculated. Above four dimensions a third phase appears for weak disorder and low-temperature ferromagnetic in nature. The transverse and longitudinal susceptibilities are discussed. Whereas the ferromagnetic transition is characterized by mean-field exponents, the ferromagnetic to spin-glass exponents are equal to their counterparts in the non-random system in d ? 2 dimensions. This is shown to originate from an effective random field proportional to the EA order parameter. The flow equations in the large-N limit are also discussed.     

The Plateau and Symmetrical Structure of Lyapunov Exponents in 2-Dimensional Homogeneous. Dissipative Map

The universal crossover behavior of Lyapunov exponents in transition from conservative limit to dissipative limit of dynamical system is studied. We discover numerically and prove analytically that for homogeneous dissipative two-dimensional maps, along the equal dissipation line in parameter space, two Lyapunov exponents λ₁ and λ₂ of periodic orbits possess a plateau structure, and around this exponent plateau value, there is a strict symmetrical relation between λ₁ and λ₂ no matter whether the orbit is periodic, quasiperiodic, or chaotic.The method calculating stable window and Lyapunov exponent plateau widths is given. For Hénon map and 2-dimensional circle map, the analytical and numerical results of plateau structure of Lyapunov exponents for period-1,2 and 3 orbits are presented.     

Lyapunov exponents in unstable systems

We investigate the dynamical behavior of unstable systems in the vicinity of the critical point associated with a liquid-gas phase transition. By considering a mean-field treatment, we first perform a linear analysis and discuss the instability growth times. Then, coming to complete Vlasov simulations, we investigate the role of nonlinear effects and calculate the Lyapunov exponents. As a main result, we find that near the critical point, the Lyapunov exponents exhibit a power-law behavior, with a critical exponent beta=0.5. This suggests that in thermodynamical systems the Lyapunov exponent behaves as an order parameter to signal the transition from the liquid to the gas phase.     

Persistence distributions in a conserved lattice gas with absorbing states

Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents are determined in two and higher dimensions. The local persistence exponent obeys a scaling relation involving the order parameter exponent of the absorbing phase transition. Furthermore we observe that the global persistence exponent exceeds its local counterpart in all dimensions in contrast to the known persistence behavior in reversible phase transitions. Received 27 August 2001 and Received in final form 15 November 2001     

Characterization of the spatial complex behavior and transition to chaos in flow systems

We introduce a “spatial” Lyapunov exponent to characterize the complex behavior of non-chaotic but convectively unstable flow sytems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that there exists a relation between the spatial-complexity index we define and the comoving Lyapunov exponents. In such systems the transition to chaos, i.e., the occurrence of a positive Lyapunov exponent, can manifest itself in two different ways. In the first case (from neither chaotic nor spatially complex behavior to chaos) one observes the typical scenario; i.e., as the system size grows up the spectrum of the Lyapunov exponents gives rise to a density. In the second case (when the chaos develops from a convectively unstable situation) one observes only a finite number of positive Lyapunov exponents.     

Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics

At zero temperature, based on the Ising model, the phase transition in a two-dimensional square lattice is studied using the generalized zero-temperature Glauber dynamics. Using Monte Carlo （MC） renormalization group methods, the static critical exponents and the dynamic exponent are studied; the type of phase transition is found to be of the first order.     

Secondary structure formation of homopolymeric single-stranded nucleic acids including force and loop entropy: Implications for DNA hybridization

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy —c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low-temperature/low-force compact (folded) structure and a high-temperature/high-force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c ≲ 2.479 a melting transition is possible; for c ≤ 2 the chain is always in the folded phase and for 2.479 ≲ c always in the unfolded phase. A force-induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single-molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double-stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ≈ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent [^(c)] \hat{{c}}, which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.     

Lyapunov exponent diagrams of a 4-dimensional Chua system

We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.     

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.     

Space-time renormalization at the onset of spatio-temporal chaos in coupled maps

The transition regime to spatio-temporal chaos via the quasiperiodic route as well as the period-doubling route is examined for coupled-map lattices. Space-time renormalization-group analysis is carried out and the scaling exponents for the coherence length, the Lyapunov exponent, and the size of the phase fluctuations are determined. Universality classes for the different types of coupling at various routes to chaos are identified.     

Explosive percolation transition is actually continuous

Recently a discontinuous percolation transition was reported in a new "explosive percolation" problem for irreversible systems [D. Achlioptas, R. M. D'Souza, and J. Spencer, Science 323, 1453 (2009)] in striking contrast to ordinary percolation. We consider a representative model which shows that the explosive percolation transition is actually a continuous, second order phase transition though with a uniquely small critical exponent of the percolation cluster size. We describe the unusual scaling properties of this transition and find its critical exponents and dimensions.     

Weak disorder expansion of Lyapunov exponents of products of random matrices: A degenerate theory

The weak disorder expansion of Lyapunov exponents of products of random matrices is derived by a new method. Our treatment can be easily generalized to the problem when in the limit of zero randomness two eigenvalues of the matrices are equal. For real degenerate matrices, the formula for the leading term of the Lyapunov exponent is derived. It has the form of a continuous fraction, which converges quickly to the exact value.     

PNJL模型下手征相变的临界指数

在PNJL模型下研究了临界点和旋节线边界上的临界指数。计算表明四个标准的临界指数$\alpha,\,\beta,\,\gamma,\,\delta$在 平均场近似下与朗道-金斯堡理论的预言一致。重子数涨落分布峰态的临界指数$\eta(\approx2)$大于偏态的 临界指数$\zeta(\approx1)$，这表明，如果在重离子碰撞实验中可以达到临界区域，峰态的测量比偏态的测量更加敏感。计算结果还表明，偏态(峰态)在旋节线边界上的临界指数与在临界点的临界指数具有相同的发散强度。根据重子数在不稳定相和亚稳相的剧烈涨落及峰态和偏态在旋节线边界上发散的特点，在将来的实验中用于鉴别一阶相变的信号在一定程度上会被干扰，一些偏离标准一阶相变的信号或许会在观测中发现。     

A model for anomalous directed percolation

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in d spatial dimensions as . Extensive numerical simulations are performed in order to determine the density exponent and the correlation length exponents and for various values of . We observe that these exponents vary continuously with , in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions. Received: 4 September 1998 / Accepted: 22 September 1998     

Critical behavior in random-spin systems with long-range interactions

Effects of the potential range of the interaction to critical behaviors of quenched random-spin systems are investigated in the limit M → 0 of the MN-component models by means of the renormalization-group theories. As static critical phenomena the stability of the fixed points is investigated and the critical exponents (η, γ, , crossover index) and the equation of state are derived. These phenomena are different from those in pure systems, for the positive specific heat exponent of the pure Heisenberg system.     

On the static and dynamic behaviour in nematic liquid crystals

Effective static exponents are calculated in the de Gennes model for isotropic-to-nematic phase transition. Applying parquet approximation we show that there are no stable fixed points for s?4. The dynamic exponent is evaluated in d?6 dimensions with the linear response theory.     

On the critical exponents for the λ transition in liquid helium

The use of a new method for summing divergent series makes it possible to significantly increase the accuracy of determining the critical exponents from the field theoretical renormalization group. The exponent value ν = 0.6700 ± 0.0006 for the λ transition in liquid helium is in good agreement with the experiment, but contradicts the last theoretical results based on using high-temperature series, the Monte Carlo method, and their synthesis.     

金属的高能二次电子发射系数与入射能量和能量幂次的关系

 根据原电子射程表达式和金属的有效真二次电子发射系数表达式,推导出金属的高能有效真二次电子发射系数与入射能量、能量幂次的关系式;并根据金属的高能有效真二次电子发射系数与金属的高能二次电子发射系数的关系,推导出金属的高能二次电子发射系数与入射能量、能量幂次的关系式。用实验数据计算出高能原电子轰击在金或银上时原电子入射能量幂次n,采用实验数据证实高能二次电子发射系数与原电子入射能量和能量幂次三者的关系,对结果进行讨论并得出结论：当高能原电子轰击在同一块金属上时,高能二次电子发射系数与原电子入射能量的n-1次幂之积近似为一常数。     

Temporal chaos versus spatial mixing in reaction-advection-diffusion systems

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of different components, is demonstrated to work accurately for time-dependent flows and different Pe clet numbers.     

Scaling law and critical exponent for α0 at the 3D Anderson transition

We use high‐precision, large system‐size wave function data to analyse the scaling properties of the multifractal spectra around the disorder‐induced three‐dimensional Anderson transition in order to extract the critical exponents of the transition. Using a previously suggested scaling law, we find that the critical exponent ν is significantly larger than suggested by previous results. We speculate that this discrepancy is due to the use of an oversimplified scaling relation.