arXiv subjects

Dmytro Shapoval

Publications and source records attributed to Dmytro Shapoval.

6 recordsLinked to original sources

arXiv2022

On the new universality class in structurally disordered $n$-vector model with long-range interactions

We study a stability border of a region where nontrivial critical behaviour of an $n$-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g. weak quenched dilution). This border is given by the marginal dimension of the order parameter $n_c$ dependent on space dimension, $d$, and a control parameter of the interaction decay, $σ$, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field-theoretical renormalization group results for the pure model with long-range interactions we get $n_c$ as a three loop $ε=2σ-d$-expansion. We provide numerical values for $n_c$ applying series resummation methods. Our results show that not only the Ising systems ($n=1$) can belong to the new disorder-induced long-range universality class at $d=2$ and $d=3$.

cond-mat.stat-mech↗

arXiv2022

Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations

We analyze the two-species reaction-diffusion system including trapping reaction $A + B \to A$ as well as coagulation/annihilation reactions $A + A \to (A,0)$ where particles of both species are performing Lévy flights with control parameter $0 < σ< 2$, known to lead to superdiffusive behaviour. The density, as well as the correlation function for target particles $B$ in such systems, are known to scale with nontrivial universal exponents at space dimension $d \leq d_{c}$. Applying the renormalization group formalism we calculate these exponents in a case of superdiffusion below the critical dimension $d_c=σ$. The numerical simulations in one-dimensional case are performed as well. The quantitative estimates for the decay exponent of the density of survived particles $B$ are in good agreement with our analytical results. In particular, it is found that the surviving probability of the target particles in a superdiffusive regime is higher than that in a system with ordinary diffusion.

cond-mat.stat-mech↗

arXiv2021

Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

We study equilibrium properties of binary lattice-gases comprising $A$ and $B$ particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials $μ_A = μ_B = μ$. The particles interact via on-site hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion for $AB$ pairs and interactions of arbitrary strength $J$, positive or negative, for $AA$ and $BB$ pairs. For tree-like Bethe and Husimi lattices, we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for $J$ being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at $μ= μ_c$ from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of $J$, this transition can be either continuous or of the first order. For sufficiently big negative $J$, the behaviour on the two lattices becomes markedly different: while for the Bethe lattice there exists a continuous transition into a phase with an alternating order followed by a continuous re-entrant transition into a disordered phase, an alternating order phase is absent on the Husimi lattice due to strong frustration effects.

cond-mat.stat-mech↗

arXiv2020

Equilibrium properties of two-species reactive lattice gases on random catalytic chains

We focus here on the thermodynamic properties of adsorbates formed by two-species $A+B \to \oslash$ reactions on a one-dimensional infinite lattice with heterogeneous "catalytic" properties. In our model hard-core $A$ and $B$ particles undergo continuous exchanges with their reservoirs and react when dissimilar species appear at neighboring lattice sites in presence of a "catalyst." The latter is modeled by supposing either that randomly chosen bonds in the lattice promote reactions (Model I) or that reactions are activated by randomly chosen lattice sites (Model II). In the case of annealed disorder in spatial distribution of a catalyst we calculate the pressure of the adsorbate by solving three-site (Model I) or four-site (Model II) recursions obeyed by the corresponding averaged grand-canonical partition functions. In the case of quenched disorder, we use two complementary approaches to find $\textit{exact}$ expressions for the pressure. The first approach is based on direct combinatorial arguments. In the second approach, we frame the model in terms of random matrices; the pressure is then represented as an averaged logarithm of the trace of a product of random $3 \times 3$ matrices -- either uncorrelated (Model I) or sequentially correlated (Model II).

cond-mat.stat-mech↗

arXiv2020

Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution

We reconsider the problem of the critical behavior of a three-dimensional $O(m)$ symmetric magnetic system in the presence of random anisotropy disorder with a generic trimodal random axis distribution. By introducing $n$ replicas to average over disorder it can be coarse-grained to a $ϕ^{4}$-theory with $m \times n$ component order parameter and five coupling constants taken in the limit of $n \to 0$. Using a field theory approach we renormalize the model to two-loop order and calculate the $β$-functions within the $\varepsilon$ expansion and directly in three dimensions. We analyze the corresponding renormalization group flows with the help of the Padé-Borel resummation technique. We show that there is no stable fixed point accessible from physical initial conditions whose existence was argued in the previous studies. This may indicate an absence of a long-range ordered phase in the presence of random anisotropy disorder with a generic random axis distribution.

cond-mat.dis-nn↗

arXiv2018

Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process

The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe lattice. On a chain, this model is exactly solvable through the empty-interval method. This method can be extended to the Bethe lattice, in the ben-Avraham-Glasser approximation. On the Bethe lattice, the analysis of the Laplace-transformed time-dependent particle-density is analogous to the study of the stationary state, if a stochastic reset to a configuration of uncorrelated particles is added. In this stationary state logarithmic corrections to scaling are found, as expected for systems at the upper critical dimension. Analogous results hold true for the time-integrated particle-density. The crossover scaling functions and the associated effective exponents between the chain and the Bethe lattice are derived.

cond-mat.stat-mech↗