Journal of Statistical Physics最新文献

We study the random-field Ising model on a Dyson hierarchical lattice, where the interactions decay in a power-law-like form, (J(r)sim r^{-alpha }), with respect to the distance. Without a random field, the Ising model on the Dyson hierarchical lattice has a long-range order at finite low temperatures when (1<alpha <2). In this study, for (1<alpha <3/2), we rigorously prove that there is a long-range order in the random-field Ising model on the Dyson hierarchical lattice at finite low temperatures, including zero temperature, when the strength of the random field is sufficiently small but nonzero. Our proof is based on Dyson’s method for the case without a random field, and the concentration inequalities in probability theory enable us to evaluate the effect of a random field.

In comparison with Derrida’s REM, we investigate the influence of the so-called decoration processes arising in the limiting extremal processes of numerous log-correlated Gaussian fields. In particular, we focus on the branching Brownian motion and two specific quantities from statistical physics in the vicinity of the critical temperature. The first one is the two-temperature overlap, whose behavior at criticality is smoothened by the decoration process—unlike the one-temperature overlap which is identical—and the second one is the temperature susceptibility, as introduced by Sales and Bouchaud, which is strictly larger in the presence of decorations and diverges, close to the critical temperature, at the same speed as for the REM but with a different multiplicative constant. We also study some general decorated cases in order to highlight the fact that the BBM has a critical behavior in some sense to be made precise.

Chang and Chen (J Stat Phys 131(4):631–650, 2008) and Chang et al. (J Stat Phys 126(3):649–667, 2007) present the number of dimer coverings and spanning trees on the Sierpinski gasket (SG_b(n)) at stage n with the side length b equal to two, three and four, respectively. In this paper, we obtain the exact closed formula of the number of dimer coverings and spanning trees on the silicate-type Sierpinski gasket (SO_b(n)) at stage n with the side length (b=2,3,4).

In this paper, we study the discrete Cucker–Smale model with a unit-speed constraint. For this, we first propose a discrete-time approximation of the Cucker–Smale model with a unit speed constraint (Choi and Ha, in: Commun Math Sci 14:953–972, 2016) using an exponential map in the state space (mathbb {R}^dtimes mathbb {S}^{d-1}). Then, we present several sufficient frameworks to guarantee its asymptotic flocking. Moreover, we prove the finite-in-time transition from the discrete system to its continuous counterpart under generic initial data and system parameters. With the help of this result and the asymptotic flocking of the discrete and continuous systems, we also demonstrate the uniform-in-time transition between them.

The asymptotic behavior of an extended family of integral geometric random functionals, including spatiotemporal Minkowski functionals under moving levels, is analyzed in this paper. Specifically, sojourn measures of spatiotemporal long-range dependence (LRD) Gaussian random fields are considered in this analysis. The limit results derived provide general reduction principles under increasing domain asymptotics in space and time. The case of time-varying thresholds is also studied. Thus, the family of morphological measures considered allows the statistical and geometrical analysis of random physical systems displaying structural changes over time. Motivated by cosmological applications, the derived results are applied to the context of sojourn measures of spatiotemporal spherical Gaussian random fields. The results are illustrated for some families of spatiotemporal Gaussian random fields displaying complex spatiotemporal dependence structures.

We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of sparse non-Hermitian random matrices (X_n) whose entries have the form (x_{jk}=d_{jk}w_{jk}) with iid complex standard Gaussian (w_{jk}) and normalised iid Bernoulli(p) (d_{jk}). It is shown that, as (prightarrow infty ), the local asymptotic behavior of the second correlation function of characteristic polynomials near (z_0in mathbb {C}) coincides with those for Ginibre ensemble: it converges to a determinant with Ginibre kernel in the bulk (|z_0|<1), and it is factorized if (|z_0|>1). For the finite (p>0), the behavior is different and exhibits the transition between different regimes depending on values of p and (|z_0|^2).

We study Hartree–Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x- and y-directions and a possibly different hopping parameter (t_z) in the z-direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases (t_z=0) and (t_z=t), respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that (t=1), we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U, and on the hopping parameter (t_z). We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as (t_z rightarrow 0). It is found that the asymptotic formulas are qualitatively different for (t_z = 0) (the two-dimensional case) and (t_z > 0) (the case of nonzero hopping in the z-direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit (t_z rightarrow 0) in which the three-dimensional model reduces to the two-dimensional model.

Focusing on a famous class of interacting diffusion processes called Ginzburg–Landau dynamics, we extend the Macroscopic Fluctuations Theory to these systems in the case where the interactions are long-range, and consequently, the macroscopic effective equations are described by non-linear fractional diffusion equations.

We study non-equilibrium properties of a chain of N oscillators with both long-ranged harmonic interactions and long-range conservative noise that exchange momenta of particle pairs. We derive exact expressions for the (deterministic) energy-current auto-correlation at equilibrium, based on the kinetic approximation of the normal mode dynamics. In all cases the decay is algebraic in the thermodynamic limit. We distinguish four distinct regimes of correlation decay depending on the exponents controlling the range of deterministic and stochastic interactions. Surprisingly, we find that long-range noise breaks down the long-range correlations characteristic of low dimensional models, suggesting a normal regime in which heat transport becomes diffusive. For finite systems, we do also derive exact expressions for the finite-size corrections to the algebraic decay of the correlation. In certain regimes, these corrections are considerably large, rendering hard the estimation of transport properties from numerical data for the finite chains. Our results are tested against numerical simulations, performed with an efficient algorithm.

We study a polynuclear growth model in which the crystallites are aligned squares, as observed in micrographs of epitaxial thin films. The expected volumes of lower layers are calculated by series expansion methods. The coefficients are calculated exactly up to the 4th power in the intensity of the nucleation process or the 12th power in the time. The method is based on exact integral expressions recently obtained by the author. The resulting instantaneous growth rate or surface speed has an initial oscillation, consistent with long-standing experimental observations. The method is also applied to 1-dimensional rod crystallites and d-dimensional cubic crystallites. For large (d) the ultimate ({text{(time}} to infty )) growth rate and oscillating growth profile are obtained. The coefficients in the series are derived from basis functions, which involve only 1-dimensional spatial integrals, and which are common to all dimensions. For the second layer, the series is derived by a cluster expansion method, analogous to methods in equilibrium statistical mechanics. For higher layers, the integrands are broken down into products of pairs of nested crystallites.