Self-averaging in the random 2D Ising ferromagnet

We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size $L$ like $\sim L \ln\ln(L)$. In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a $\delta$-peak in the thermodynamic limit $L \to \infty$. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.Comment: 12 pages, accepted versio

The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius

We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a directed polymer with delta-correlated random potential can be applied for the description of the present system only in the high-temperature limit. For the low temperature limit we have obtained the new solution which is described by the one-step replica symmetry breaking. For the mean square deviation of the directed polymer of the linear size L it provides the usual scaling $L^{2z}$ with the wandering exponent z = 2/3 and the temperature-independent prefactor.Comment: 14 pages, Late

Scaling Relations for Logarithmic Corrections

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such logarithms and to propose scaling relations between them. These proposed relations are then confronted with a variety of results from the literature.Comment: 4 page

Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat's logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios - logarithmic corrections versus weak universality - strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.Comment: 10 pages, 8 figures, slightly revised version as accepted for publication in Phys. Rev.

Water Resources Management In Support Of Raw Region Based On Decoupling Effect

It determines the presence of the decoupling effect in the Russians raw regions materials by using water. Developed models that explain the relationship between the gross regional product and water intake. It proved no effect on the growth of water consumption in most regions of the reference commodity. Recommendations for the decoupling effect development in support of Russians raw regions

Kink pairs unbinding on domain walls and the sequence of phase transitions in fully frustrated XY models

The unbinding of kink pairs on domain walls in the fully frustrated XY model (on square or triangular lattices) is shown to induce the vanishing of phase coupling across the walls. This forces the phase transition, associated with unbinding of vortex pairs to take place at a lower temperature than the other phase transition, associated with proliferation of the Ising-type domain walls. The results are applicable for a description of superconducting junction arrays and wire networks in perpendicular magnetic field (corresponding to half-integer number of flux quanta per each lattice plaquette), as well as of planar antiferromagnets with a triangular lattice.Comment: 4 pages, ReVTeX, the final versio

The dynamics of near-surface prismatic loops in lead

The paper proposes the study of the dynamics of near-surface dislocation loops in lead. It has been shown that the activation of a prismatic near-surface dislocation loop and its motion inward the crystal practically throughout the entire path occurs at a high velocity close to the speed of sound in metal. The kinetic energy per unit length of the dislocation loop during its motion decreases linearly and weakly depends on the density of dislocations in metal. Moreover, a weak dependence of the path length and the path time of a prismatic loop on the dislocation density in lead is observed

On the nature of the phase transition in the three-dimensional random field Ising model

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. Nature of the phase transition in the three-dimensional RFIM with Gaussian random fields is discussed. Using simple scaling arguments it is shown that if the strength of the random fields is not too small (bigger than a certain threshold value) the finite temperature phase transition in this system is equivalent to the low-temperature order-disorder transition which takes place at variations of the strength of the random fields. Detailed study of the zero-temperature phase transition in terms of simple probabilistic arguments and modified mean-field approach (which take into account nearest-neighbors spin-spin correlations) is given. It is shown that if all thermally activated processes are suppressed the ferromagnetic order parameter m(h) as the function of the strength $h$ of the random fields becomes history dependent. In particular, the behavior of the magnetization curves m(h) for increasing and for decreasing $h$ reveals the hysteresis loop.Comment: 22 pages, 12 figure

Self-consistent scaling theory for logarithmic-correction exponents

Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made.Comment: 4 pages, to appear in Phys.Rev.Let