Search arXivSearch

arXiv · 1104.4388

Collective surface diffusion near a first-order phase transition

Abstract

For a large class of lattice models we study the thermodynamic factor, $Φ$, of the collective surface diffusion coefficient near a first-order phase transition between two phases at low temperatures. In a two-phase regime its dependence on the coverage, $\te$, is $Φ\approx \te/[(\te-\te_-)(\te_+ - \te)N]$, where $N$ is the number of adsorption sites and $\te_\pm$ are the single-phase coverages at the transition. In the crossover between the two-phase and single-phase regimes $Φ(\te)$ is shown to have a more complex behavior. The results are applied to a simple 2D lattice model.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Igor Medved', Anton Trník. 2011-04-22. Collective surface diffusion near a first-order phase transition. https://doi.org/10.1103/physrevb.83.233406

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Heider balance in square versus triangular lattices under an external field

We discuss the Heider model in the presence of an external social field. This field breaks the possible symmetry between the probabilities of hostile and friendly relationships. We consider the system in the presence of fluctuations generated by thermal noise and present the results of a comparative study of two-dimensional triangular and square networks with periodic boundary conditions. The results were obtained using three different methods: exact calculations for small systems ($3 \times 3$ square lattice and $2 \times 2$ triangular lattice), Monte Carlo simulations of medium-sized systems ($16 \times 16$ lattices), and exact calculations in the thermodynamic limit (corresponding to infinite size) of certain limiting cases for which analytical solutions are possible. In particular, we exploit the recently discovered equivalence between structurally balanced systems and the Ising model to derive an exact form of the edge magnetization susceptibility for systems in Heider equilibrium.

cond-mat.stat-mech

Robust q-negative Multifractal Detrended Cross-Correlation Coefficient

The multifractal detrended cross-correlation coefficient $ρ_q(n)$ is widely used to investigate scale-dependent interactions, but its application to negative fluctuation orders is affected by numerical instabilities, unbounded values, and interpretational difficulties. We propose a Signed Multifractal Detrended Cross-Correlation Coefficient, $ρ_{\mathrm{SMFDCCA}}(n,q)$, an amplitude-conditioned correlation observable for multifractal detrended analysis, based on locally normalized detrended correlations and regularized fluctuation amplitudes. The proposed coefficient preserves the sign of local interactions, remains strictly bounded within $[-1,1]$ for both positive and negative values of $q$, and eliminates the corrective procedures required by previous approaches. Validation using independent fractional Gaussian noise confirms the absence of spurious cross-correlations and the numerical stability of the method. Applications demonstrate that the proposed observable resolves how cross-correlations evolve jointly with temporal scale and fluctuation amplitude, revealing scale- and amplitude-dependent correlation structures, including stronger synchronization during large fluctuations in stock-market indices and heterogeneous coupling patterns in temperature records.

cond-mat.stat-mech

Branching stochastic mechanics: Clustering and connected correlations within a branching-process representation of the Schrödinger equation

Can finite-range correlations hide in the statistics of an extended quantum state? The Schrödinger-Nagasawa transform represents the wave function by positive forward and backward diffusion fields whose product is the Born density. We promote them to branching superprocesses, \(Φ_F\) and \(Φ_B\): diffusion samples stochastic paths, whereas Bohm/Fisher-controlled branching generates genealogies of alternative continuations. With rates evaluated on the prescribed Born density, their means reproduce Schrödinger dynamics exactly. The connected sector exhibits supercritical, critical, and subcritical clustering in confinement and has critical dimension \(d_c=2\) in free space. Stationary eigenmodes remain extended; subcritical clusters acquire the reduced de~Broglie scale. We then let the branching rate respond to the fluctuating product \(Φ_FΦ_B\). In the reciprocal basis, the fields equal a smooth reference \(R\) plus centered fluctuations \(ψ_F,ψ_B\), defining the signed kernel \(C_{\rm FB}(x,y)=\mathbb E_ω[ψ_F(x)ψ_B(y)]\). On the anticorrelated branch, \(ρ_{\rm BSM}(x)=-C_{\rm FB}(x,x)\) is the positive organized connected weight. Stationary matching of this weight to the Born profile is imposed as a closure condition, while off-diagonal decay defines the correlation range. The pair equation splits into collective and relative sectors: spectral cancellation selects the Born collective mode, while suppression of the leading density fluctuation selects the anticorrelated source channel. With relative diffusivity \(D_{\rm eff}\) and positive relaxation rate \(μ_{\rm FB}\), correlations have screening length \(ξ_{\rm FB}=\sqrt{D_{\rm eff}/μ_{\rm FB}}\). Within this reciprocal closure, an extended Born-shaped connected weight and a finite correlation range can coexist in one stochastic kernel.

cond-mat.stat-mech