SEARCH · Searcharxiv

Results for “cond-mat”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,477 records · Page 82Linked to original sources

arXiv1996

Near-Surface Long-Range Order at the Ordinary Transition: Scaling Analysis and Monte Carlo Results

Motivated by recent experimental activities on surface critical phenomena, we present a detailed theoretical study of the near-surface behavior of the local order parameter m(z) in Ising-like spin systems. Special attention is paid to the crossover regime between ``ordinary'' and ``normal'' transition in the three-dimensional semi-infinite Ising model, where a finite magnetic field H_1 is imposed on the surface which itself exhibits a reduced tendency to order spontaneously. As the theoretical foundation, the spatial behavior of m(z) is discussed by means of phenomenological scaling arguments, and a finite-size scaling analysis is performed. Then we present Monte Carlo results for m(z) obtained with the Swendsen-Wang algorithm. In particular the power-law increase of the magnetization, predicted for a small H_1 by previous work of the authors, is corroborated by the numerical results. The relevance of these findings for experiments on critical adsorption in systems where a small effective surface field occurs is pointed out.

cond-mat↗

arXiv1997

Percolation and Cluster Formalism in Continuous Spin Systems

The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate percolative characteristics, the new cluster definition is analytically explored in one dimension and with Monte Carlo simulations in 2D and 3D frustrated and unfrustrated n-clock models. In these models (also in unfrustrated cases for large n) the percolative transition temperature is higher than the usual thermodynamical critical one.

cond-mat↗

arXiv1996

Numerical simulations of scattering speckle from phase ordering systems

The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be used to study the dynamics of the system. Here we report large-scale computer simulations of the speckle dynamics for a phase ordering system, using a two-dimensional model quenched through an order--disorder transition into the two-phase regime. The intensity at each wave vector ${\bf k}$ is found to be an exponentially distributed random variable. The scaling hypothesis is extended to the two-time correlation function of the scattering intensity at a given wave vector, $Corr({\bf k};t_1,t_2)$. The characteristic decay time difference for the correlation function, $|t_1 - t_2|_c$, is found to scale as $k|t_1 + t_2|^{1/2}$.

cond-mat↗

arXiv1997

Simulated Annealing with Tsallis Weights - A Numerical Comparison

We discuss the use of Tsallis generalized mechanics in simulated annealing algorithms. For a small peptide it is shown that older implementations are not more effective than regular simulated annealing in finding ground state configurations. We propose a new implementation which leads to an improvement over regular simulated annealing.

cond-mat↗

arXiv1997

Random Matrix Theory by the Supersymmetry Method Beyond the Sigma-Model

The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the supersymmetry method is extended beyond the sigma-model, to include small quadratic fluctuations around the saddle point. Special care is taken to avoid the potential divergence arising from the unbounded nature of the saddle point. Also, in the small energy difference regime, the leading correction to a two point correlation function is obtained.

cond-mat↗

arXiv1997

Fluctuations around Nash Equilibria in Game Theory

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players' interactions so that huge fluctuations can results from a small amount of irrationality. In the presence of multiple Nash equilibria, our statistical approach allows to establish which is the globally stable equilibrium. However characteristic times to reach this state can be very large.

cond-mat↗

arXiv1997

The Interface Tension of the 3-Dimensional Ising Model in the Scaling Region

Using the Monte Carlo method, we determine the free energy of the interface of the 3D Ising model in the scaling region. By integrating the interface energies over the inverse temperature $β$, we obtain estimates for the free energies of interfaces with cross sections up to 96 by 96, and for a range $0.223 \leq β\leq 0.23$. Our data yield a precise estimation of the interface tensions $σ$. We determine the amplitude $σ_0$ in the critical law $σ\sim σ_0 t^μ$ and estimate the combination $σξ^2$ which yields the universal constant $R_{-}$ in the critical limit.

cond-mat↗

arXiv1997

Large financial crashes

We propose that large stock market crashes are analogous to critical points studied in statistical physics with log-periodic correction to scaling. We extend our previous renormalization group model of stock market prices prior to and after crashes [D. Sornette et al., J.Phys.I France 6, 167, 1996] by including the first non-linear correction. This predicts the existence of a log-frequency shift over time in the log-periodic oscillations prior to a crash. This is tested on the two largest historical crashes of the century, the october 1929 and october 1987 crashes, by fitting the stock market index over an interval of 8 years prior to the crashes. The good quality of the fits, as well as the consistency of the parameter values obtained from the two crashes, promote the theory that crashes have their origin in the collective ``crowd'' behavior of many interacting agents.

cond-mat↗

arXiv1997

The short-time behaviour of a kinetic Ashkin-Teller model on the critical line

We simulate the kinetic Ashkin-Teller model with both ordered and disordered initial states, evolving in contact with a heat-bath at the critical temperature. The power law scaling behaviour for the magnetic order and electric order are observed in the early time stage. The values of the critical exponent $θ$ vary along the critical line. Another dynamical exponent $z$ is also obtained in the process.

cond-mat↗

arXiv1996

Renormalization Group Study of Sandpile on the Triangular Lattice

We apply the renormalization group approach to the sandpile on the triangular lattice. The only attractive fixed point is found. The obtained fixed point height probabilities are compared with numerical simulations. The value of critical exponent of avalanche size distribution is found to be $τ=1.36$. The probabilities of the sand transition are compared with the branching probabilities of the spanning trees on the triangular lattice which are also evaluated.

cond-mat↗

arXiv1996

Repulsive particles on a two-dimensional lattice

The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as described by the spinless Falicov-Kimball model. For a range of particle density including the half-filled case, it is shown that the minimum-energy states coincide with the large-U neutral ground state ionic configurations of the Falicov-Kimball model, thus providing a characterization of the latter as ``most homogeneous'' ionic arrangements. These obey hierarchical rules, leading to a sequence of phases described by the Farey tree. For lower densities, a new family of minimum-energy configurations is found, having the novel property that they are aperiodic even when the particle density is a rational number. In some cases there occurs local phase separation, resulting in an inherent sensitivity of the ground state to the detailed form of the interaction potential.

cond-mat↗

arXiv1998

A hierarchical scheme for cooperativity and folding in proteins

We propose a protein model based on a hierarchy of constraints that force the protein to follow certain pathways when changing conformation. The model exhibits a first order phase transition, cooperativity and is exactly solvable. It also shows an unexpected symmetry between folding and unfolding pathways as suggested by a recent experiment.

cond-mat↗

arXiv1997

Numerical simulations of a two-dimensional lattice grain boundary model

We present detailed Monte Carlo results for a two-dimensional grain boundary model on a lattice. The effective Hamiltonian of the system results from the microscopic interaction of grains with orientations described by spins of unit length, and leads to a nearest-neighbour interaction proportional to the absolute value of the angle between the grains. Our analysis of the correlation length xi and susceptibility chi in the high-temperature phase favour a Kosterlitz-Thouless-like (KT) singularity over a second-order phase transition. Unconstrained KT fits of chi and xi confirm the predicted value for the critical exponent nu, while the values of eta deviate from the theoretical prediction. Additionally we apply finite-size scaling theory and investigate the question of multiplicative logarithmic corrections to a KT transition. As for the critical exponents our results are similar to data obtained from the XY model, so that both models probably lie in the same universality class.

cond-mat↗

arXiv1997

Numerical Analysis of the Bond-Random Antiferromagnetic S=1 Heisenberg Chain

Ground state of the bond-random antiferromagnetic S=1 Heisenberg chain with the biquadratic interaction -β\sum_i(S_i S_i+1)^2 is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase β\sim0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremely-broad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.

cond-mat↗

arXiv1998

Quantum Corrections for Generalized Partition Functions

The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order quantum corrections are worked out explicitly, and the classical limit for the Tsallis thermostatistics is determined. The results of this work generalize the ones obtained by E. Wigner (Phys. Rev. 40 (1932) 749) for usual statistical mechanics.

cond-mat↗

arXiv1997

Wetting of Curved Surfaces

As a first step towards a microscopic understanding of the effective interaction between colloidal particles suspended in a solvent we study the wetting behavior of one-component fluids at spheres and fibers. We describe these phenomena within density functional theory which keeps track of the microscopic interaction potentials governing these systems. In particular we properly take into account the power-law decay of both the fluid-fluid interaction potentials and the substrate potentials. The thicknesses of the wetting films as a function of temperature and chemical potential as well as the wetting phase diagrams are determined by minimizing an effective interface potential which we obtain by applying a sharp-kink approximation to the density functional. We compare our results with previous approaches to this problem.

cond-mat↗

arXiv1997

Beyond the Hubbard-I Solution with a One-Pole Self-Energy at Half-Filling with the Moment Approach: Non-Linear Effects

We have postulated a single pole for the self-energy, $Σ(\vec{k},ω)$, looking for the consequences on the one-particle Green function, $G(\vec{k},ω)$ in the Hubbard model. We find that $G(\vec{k},ω)$ satisfies the first two sum rules or moments of Nolting (Z. Physik 255, 25 (1972)) for any values of the two unknown $\vec{k}$ parameters of $Σ(\vec{k},ω)$. In order to find these two parameters we have used the third and four sum rules of Nolting. $G(\vec{k},ω)$ turns out to be identical to the one of Nolting (Z. Physik 225, 25 (1972)), which is beyond a Hubbard-I solution since satisfies four sum rules. With our proposal we have been able to obtain an expansion in powers of $U$ for the self-energy (here to second order in $U$). We present numerical results at half-filling for 1- the static spin susceptibility, $χ(T)$ vs $T/t$ and 2- the band narrowing parameter, $B(T)$ vs $T/t$. The two-pole Ansatz of Nolting for the one-particle Green function is equivalent to a single pole Ansatz for the self-energy which remains the fundamental quantity for more elaborated calculations when, for example, lifetime effects are included.

cond-mat↗

arXiv1998

Random-field-driven phase transitions in the ground state of the S=1 XXZ spin chain

Ground-state of the S=1 XXZ spin chain under the influence of the random magnetic field is studied by means of the exact-diagonalization method. The S=1/2 counterpart has been investigated extensively so far. The easy-plane area, including the Haldane and the XY phases, is considered. The area suffers significantly from the magnitude of the constituent spin. Destruction of the Haldane state is observed at a critical strength of the random field, which is comparable to the magnitude of the Haldane gap. This transition is characterized by the disappearance of the string order. The XY region continues until at a critical randomness, at which a transition of the KT-universality class occurs. These features are contrasted with those of the S=1/2 counterpart.

cond-mat↗