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arXiv2013

Completeness and Bethe root distribution of the spin-1/2 Heisenberg chain with arbitrary boundary fields

Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one choice of the parameterizations [3]. In this paper, we discuss further the completeness of another parameterization of the Bethe ansatz equations and its reduction to the parallel boundary field case. The numerical results show that when the relative angle between the boundary fields turns to zero, both the T-Q relations and the Bethe ansatz equations are reduced to the ones obtained by the conventional Bethe ansatz methods. This allows us to establish a one-to-one correspondence between the Bethe roots of the unparallel boundary field case and those of the parallel boundary field case. In the thermodynamic limit, those two sets of Bethe roots tend to the same and the contribution of the relative angle to the energy is in the order of 1/N.

cond-mat.stat-mech↗
arXiv2013

A new transfer-matrix algorithm for exact enumerations: self-avoiding walks on the square lattice

We recently published [J. Phys A: Math. Theor. {\bf 45} 115202 (2012)] a new and more efficient implementation of a transfer-matrix algorithm for exact enumerations of self-avoiding polygons. Here we extend this work to the enumeration of self-avoiding walks on the square lattice. A detailed comparison with our previous best algorithm shows very significant improvement in the running time of the new algorithm. The new algorithm is used to extend the enumeration of self-avoiding walks to length 79 from the previous record of 71 and for metric properties, such as the average end-to-end distance, from 59 to 71.

math-ph↗
arXiv2013

Four variants of theory of the second order phase transitions

Because of one-valued connection between the configurational entropy and the order parameter it is possible to present the theory of the second order phase transitions in terms of the configurational entropy. It is offered a variant of theory, in which the Nernst theorem is obeyed. Within the framework of heterogeneous model the phenomena of growth of level of fluctuations and their correlations are analyzed at transition of critical point as competitions of kinetic and relaxation processes in the conditions of proximity of two critical points.

cond-mat.stat-mech↗
arXiv2013

Density-temperature scaling of the fragility in a model glass-former

Dynamical quantities such as the diffusion coefficient and relaxation times for some glass-formers may depend on density and temperature through a specific combination, rather than independently, allowing the representation of data over ranges of density and temperature as a function of a single scaling variable. Such a scaling, referred to as density - temperature (DT) scaling, is exact for liquids with inverse power law (IPL) interactions but has also been found to be approximately valid in many non-IPL liquids. We have analyzed the consequences of DT scaling on the density dependence of the fragility in a model glass-former. We find the density dependence of kinetic fragility to be weak, and show that it can be understood in terms of DT scaling and deviations of DT scaling at low densities. We also show that the Adam-Gibbs relation exhibits DT scaling and the scaling exponent computed from the density dependence of the activation free energy in the Adam-Gibbs relation, is consistent with the exponent values obtained by other means.

cond-mat.stat-mech↗
arXiv2013

Why asymmetric interparticle interaction can result in convergent heat conductivity

We show that the asymmetric inter-particle interactions may induce rapid decay of heat current autocorrelation in one-dimensional momentum conserving lattices. When the asymmetry degree and the temperature are appropriate, the decay is sufficient rapid for resulting a convergence conductivity practically. To understand the underlying mechanism, we further studied the relaxation behavior of the hydrodynamic modes. It is shown that for lattice with symmetric potential, the heat mode relaxs in the superdiffusive manner, while in the case of asymmetric potential, the heat mode may relax in the normal manner.

cond-mat.stat-mech↗
arXiv2013

Status of the Clausius inequality in classical thermodynamics

We present an analysis of the foundations of the well known Clausius inequality. It is shown that, strictly speaking, the inequality is not a logical consequence of the Kelvin-Planck formulation of the second law of thermodynamics. Some thought experiments demonstrating the violation of the Clausius inequality are considered. Also, a reformulation of the Landauer's principle in terms of the Clausius inequality is proposed. This version of the inequality may be considered a consequence of the fluctuation theorem.

physics.class-ph↗
arXiv2013

Magnetic Properties of Two-dimensional Nanodots: Ground State and Phase Transition

We study the effect of perpendicular single-ion anisotropy, $-As_{\text{z}}^2$, on the ground-state structure and finite-temperature properties of a two-dimensional magnetic nanodot in presence of a dipolar interaction of strength $D$. By a simulated annealing Monte Carlo method, we show that in the ground state a vortex core perpendicular to the nanodot plane emerges already in the range of moderate anisotropy values above a certain threshold level. In the giant-anisotropy regime the vortex structure is superseded by a stripe domain structure with stripes of alternate domains perpendicular to the surface of the sample. We have also observed an intermediate stage between the vortex and stripe structures, with satellite regions of tilted nonzero perpendicular magnetization around the core. At finite temperatures, at small $A$, we show by Monte Carlo simulations that there is a transition from the the in-plane vortex phase to the disordered phase characterized by a peak in the specific heat and the vanishing vortex order parameter. At stronger $A$, we observe a discontinuous transition with a large latent heat from the in-plane vortex phase to perpendicular stripe ordering phase before a total disordering at higher temperatures. In the regime of perpendicular stripe domains, namely with giant $A$, there is no phase transition at finite $T$: the stripe domains are progressively disordered with increasing $T$. Finite-size effects are shown and discussed.

cond-mat.stat-mech↗
arXiv2013

Influence of random pinning on the crystallization process in suspensions of hard spheres

We discuss crystal formation in supersaturated suspensions of monodisperse hard spheres with a concentration of hard spheres randomly pinned in space and time. The pinning procedure introduces an external length scale and an external time scale that restrict the accessible number of configurations and ultimately the number of pathways leading to crystallization. We observe a significant drop in the nucleation rate density at a characteristic pinning concentration that can be directly related to the structure of the critical nucleus and the dynamics of its formation in the unpinned system.

cond-mat.stat-mech↗
arXiv2013

A trivial non-chaotic map lattice asymptotically indistiguishable from a Lévy walk

In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property and the vanishing Lyapunov exponents are intended to mimic the dynamics of polygonal billiards, which are known to give rise to anomalous diffusion, but which are too complicated to be analyzed as thoroughly as desired. Depending on the value taken by a single parameter α, our map experiences sub-diffusion, super-diffusion or normal diffusion. Therefore its transport properties can be compared with those of given Lévy walks describing transport in quenched disordered media. Fixing α so that the mean square displacement generated by our map and that generated by the corresponding Lévy walk asymptotically coincide, we prove that all moments of the corresponding asymptotic distributions coincide as well, hence all observables which are expressed in terms of the moments coincide.

math-ph↗
arXiv2013

Microscopic Derivation of an Isothermal Thermodynamic Transformation

We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a varying tension (external force) and the contact with the heat bath is modeled by independent Langevin dynamics acting on each particle. After a diffusive space-time scaling and cross-graining, the profile of volume converges to the solution of a deterministic diffusive equation with boundary conditions given by the applied tension. This defines an irreversible thermodynamic transformation from an initial equilibrium to a new equilibrium given by the final tension applied. Quasi static reversible isothermal transformations are then obtained by a further time scaling. Heat is defined as the total flux of energy exchanged between the system and the heat bath. Then we prove that the relation between the limit heat, work, free energy and thermodynamic entropy agree with the first and second principle of thermodynamics.

cond-mat.stat-mech↗
arXiv2013

Comment on "Possible divergences in Tsallis' thermostatistics"

The problematic divergence of the $q$-partition function of the harmonic oscillator recently considered in \cite{plastino} is a particular case of the non-normalizabilty of the distribution function of classical Hamiltonian systems in non-extensive thermostatistics as discussed previously in \cite{lutsko-boon}.

cond-mat.stat-mech↗
arXiv2013

Kramers-Wannier Duality of Statistical Mechanics Applied to the Boolean Satisfiability Problem of Computer Science

We present a novel application of the Kramers-Wannier duality on one of the most important problems of computer science, the Boolean satisfiability problem (SAT). More specifically, we focus on sharp-SAT or equivalently #SAT - the problem of counting the number of solutions to a Boolean satisfaction formula. #SAT can be cast into a statistical-mechanical language, where it reduces to calculating the partition function of an Ising spin Hamiltonian with multi-spin interactions. We show that Kramers-Wannier duality can be generalized to apply to such multi-connected spin networks. We present an exact dual partner to #SAT and explicitly verify their equivalence with a few simple examples. It is shown that the NP-completeness of the original problem maps on the complexity of the dual problem of enumerating the number of non-negative solutions to a Diophantine system of equations. We discuss the implications of this duality and the prospects of similar dualities applied to computer science problems.

cond-mat.stat-mech↗
arXiv2013

Multifractal analysis of three-dimensional grayscale images: Estimation of generalized fractal dimension and singularity spectrum

A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour is described. Then, in order to characterize the 3D system, the theoretical calculation of the generalized fractal dimension and two different approaches for evaluating the singularity spectrum are presented.

cond-mat.stat-mech↗
arXiv2013

Bond-Alternation-Induced Topological Quantum Gaussian Transition and Topological Quantum Crossover in Ising Chains with the Dzyaloshinskii-Moriya Interaction

Non-local orders, entanglement entropy, and quantum fidelity are investigated in an infinite-size bond-alternating Ising chain with the Dzyaloshinskii-Moriya interaction by employing the infinite matrix product state representation with the infinite time evolving block decimation method. Directly computing two distinct types of finite string correlations for very large lattice distances, in contrast to an extrapolated extreme value for finite size chains, reveals two topologically ordered phases. As the bond alternation varies, a topological quantum phase transition with continuously variable critical exponents along the phase boundary occurs between the two Haldane phases for the Dzyaloshinskii-Moriya interaction stronger than the Ising interaction, while a topological quantum crossover between them happens through an intermediate antiferromagentic phase demonstrated with the quantum fidelity for the Dzyaloshinskii-Moriya interaction weaker than the Ising interaction. The critical exponents of the order parameters and the central charges from the entanglement entropy quantify the universality classes of the phase transition points. Anisotropic Heisenberg types of spin chains with bond alternations are finally discussed to share the same criticality.

cond-mat.str-el↗
arXiv2013

Invariant Energy Levels and Flat Band Engineering in a Kondo Lattice Model on Geometrically Frustrated Lattices

We show the existence of invariant energy levels in a Kondo lattice model on an isolated complete graph, such as a triangle and a tetrahedron. These energy levels always have fixed eigenenergies $t \pm J/2$, irrespective of the configuration of localized moments ($t$ is the transfer integral of conduction electrons and $J$ is the spin-charge coupling constant). We also extend the analysis to geometrically frustrated lattices by using the complete graphs as basic building blocks. We show that the construction rule for the invariant energy levels leads to the existence condition of localized states, if the model is defined on the triangle-based line graphs, such as a kagome lattice. We further propose a procedure of engineering isolated flat bands with broken time-reversal symmetry, which are separated from other dispersive bands with finite energy gaps.

cond-mat.str-el↗
arXiv2013

Lindblad equation for a non-interacting fermionic system: full-counting statistics

We develop a method of calculating the full-counting statistics for a non-interacting fermionic system coupled to the memory-less reservoirs. The evolution of the system is described by the Lindblad equation. By the basis change the Liouvillian operator is brought to the quadratic form. This allows us a straightforward calculation of any observable in the non-equilibrium steady state. We introduce the counting field in the Lindblad equation which brings us to the generating function and helps us to obtain all cumulants of the charge transport. For the two-site system we give the expression for the generating function. For system longer than two sites we perform numerical investigations which suggest that it in a uniform system the cumulants of order $k$ are independent of the size of the system for system sizes larger $k+1$. The counting statistics from the Lindblad approach does not take into account interference in the reservoirs which gives a decreased noise in comparison with the Green function method which describes phase coherent leads. The current obtained by two methods is the same, which relies on the current conservation. The Fano factors are different (with a linear relation connecting them) and allow to distinguish between memory-less and phase coherent reservoirs.

cond-mat.mes-hall↗
arXiv2013

Internal DLA for cylinders

We show that space-time averages of the fluctuations of internal DLA on a cylinder Z_N x Z converge in law to the Gaussian free field.

math.PR↗