arXiv subjects

O. A. Vasilyev

Publications and source records attributed to O. A. Vasilyev.

11 recordsLinked to original sources

arXiv2026

Spin-$s$ model with competing interactions on diamond-decorated lattices

We investigate the ground state properties, magnetization, and low-temperature thermodynamics of the ferromagnetic-antiferromagnetic spin-$s$ model on diamond-decorated lattices with ideal diamond units, incorporating bilinear Heisenberg and higher-order exchange interactions between diagonal spins-$σ$. Local conservation of the composite spin on each diamond diagonal enables exact analysis. For the pure Heisenberg case, the system undergoes a series of $2σ$ transitions between monomer-dimer (MD), ferrimagnetic (Ferri) and ferromagnetic (F) phases with different optimal composite spin values as the coupling ratio varies. In the presence of higher-order interactions, a multicritical point exists where the states with all possible values of composite spin are degenerate, leading to maximal ground state degeneracy. The case $s=σ=1$ with bilinear and biquadratic interactions is studied in detail. Its phase diagram comprises three phases - F, Ferri and MD, which meet at a triple point. On the phase boundaries, the ground state becomes macroscopically degenerate. For the diamond chain, we calculate the ground state degeneracy exactly; for higher dimensions, the problem maps onto a bond percolation framework, solved numerically. The residual entropy per spin reaches up to $60\%$ of the maximal value, peaking at the triple point. Low-temperature magnetization curves in external magnetic fields exhibit plateaus and jumps. The excitation spectrum is gapped in the MD phase, gapless in the F phase, and resembles that of the Lieb-Mattis ferrimagnet in the Ferri phase. The high residual entropy suggests potential applications in ultra-low-temperature cooling and quantum thermal machines.

cond-mat.str-el↗

arXiv2026

Frustrated spin models on two- and three-dimensional decorated lattices with high residual entropy

We study the ground-state properties of a family of frustrated spin-1/2 Heisenberg models on two- and three-dimensional decorated lattices composed of connected star-shaped units. Each star is built from edge-sharing triangles with an antiferromagnetic interaction on the shared side and ferromagnetic interactions on the others. At a critical coupling ratio, the ideal star model - defined by equal ferromagnetic interactions - exhibits a macroscopically degenerate ground state, which we map onto a site percolation problem on the Lieb lattice. This mapping enables the calculation of exponential ground-state degeneracy and the corresponding residual entropy for square, triangular, honeycomb, and cubic lattices. Remarkably, the residual entropy remains high for all studied lattices, exceeding 60\% of the maximal value ln(2). Despite a gapless quadratic one-magnon spectrum, the low-temperature thermodynamics is governed by exponentially numerous gapped excitations. For a distorted-star variant of the model, the ground-state manifold is equivalent to that of decoupled ferromagnetic clusters, leading to exponential degeneracy with a lower, yet still substantial, residual entropy. At low temperature the system mimics a paramagnetic crystal of non-interacting spins with high spin value ($s=4$ for a square lattice). The obtained results establish a structural design principle for engineering quantum magnets with a high ground-state degeneracy, suggesting promising candidates for enhanced magnetocaloric cooling and quantum thermal machines.

cond-mat.str-el↗

arXiv2026

Phase diagram and macroscopic ground state degeneracy of frustrated spin-1/2 anisotropic Heisenberg model on diamond-decorated lattices

We study the ground state properties of the anisotropic spin-1/2 Heisenberg model on lattices built from ideal diamond units with competing ferro- and antiferromagnetic interactions. The study covers the one-dimensional diamond chain and its two- and three-dimensional generalizations. The ground-state phase diagram contains four distinct phases: ferromagnetic (F), critical (C), monomer-dimer (MD), and tetramer-dimer (TD), which converge at a quadruple point. We demonstrate the presence of macroscopic ground-state degeneracy and corresponding residual entropy, which is maximal at the quadruple point and also extends throughout the MD phase and its boundaries with TD and F phases. For the diamond chain, we derive exact degeneracies, while for higher-dimensional lattices, we map the problem onto a bond percolation model or used transfer-matrix approach, enabling the numerical computation of the ground state degeneracy.

cond-mat.str-el↗

arXiv2025

Macroscopic ground state degeneracy of the ferro-antiferromagnetic Heisenberg model on diamond-decorated lattices

We investigate the spin-1/2 Heisenberg model with competing ferromagnetic and antiferromagnetic interactions on diamond-decorated lattices. Tuning the exchange interactions to the boundary of the ferromagnetic phase, we analyze the models with two types of diamond units: distorted and ideal diamonds. In the distorted diamond model, flat bands in the magnon spectra indicate the localized states confined to small regions (`trapping cells') of the lattice. Remarkably, these trapping cells can host up to five and seven localized states for square and cubic lattices, respectively, leading to the macroscopic ground state degeneracy and high value of residual entropy. The problem of calculating ground state degeneracy reduces to that of non-interacting spins, whose spin value equal to half the number of localized magnons in the trapping cell. In contrast, ideal diamond models feature ground states composed of randomly distributed isolated diamond diagonal singlets immersed in a ferromagnetic background. Counting the ground state degeneracies here maps onto the percolation problem in 2D and 3D lattices. Our analysis shows that ideal diamond models possess even greater ground state degeneracy than their distorted counterparts. These findings suggest that synthesizing diamond-decorated-type compounds holds great promise for low-temperature cooling applications.

cond-mat.str-el↗

arXiv2019

Current-mediated synchronization of a pair of beating non-identical flagella

The basic phenomenology of experimentally observed synchronization (i.e., a stochastic phase locking) of identical, beating flagella of a biflagellate alga is known to be captured well by a minimal model describing the dynamics of coupled, limit-cycle, noisy oscillators (known as the noisy Kuramoto model). As demonstrated experimentally, the amplitudes of the noise terms therein, which stem from fluctuations of the rotary motors, depend on the flagella length. Here we address the conceptually important question which kind of synchrony occurs if the two flagella have different lengths such that the noises acting on each of them have different amplitudes. On the basis of a minimal model, too, we show that a different kind of synchrony emerges, and here it is mediated by a current carrying, steady-state; it manifests itself via correlated "drifts" of phases. We quantify such a synchronization mechanism in terms of appropriate order parameters $Q$ and $Q_{\cal S}$ - for an ensemble of trajectories and for a single realization of noises of duration ${\cal S}$, respectively. Via numerical simulations we show that both approaches become identical for long observation times ${\cal S}$. This reveals an ergodic behavior and implies that a single-realization order parameter $Q_{\cal S}$ is suitable for experimental analysis for which ensemble averaging is not always possible.

cond-mat.soft↗

arXiv2013

Critical Casimir Forces for Films with Bulk Ordering Fields

The confinement of long-ranged critical fluctuations in the vicinity of second-order phase transitions in fluids generates critical Casimir forces acting on confining surfaces or among particles immersed in a critical solvent. This is realized in binary liquid mixtures close to their consolute point $T_{c}$ which belong to the universality class of the Ising model. The deviation of the difference of the chemical potentials of the two species of the mixture from its value at criticality corresponds to the bulk magnetic filed of the Ising model. By using Monte Carlo simulations for this latter representative of the corresponding universality class we compute the critical Casimir force as a function of the bulk ordering field at the critical temperature $T=T_{c}$. We use a coupling parameter scheme for the computation of the underlying free energy differences and an energy-magnetization integration method for computing the bulk free energy density which is a necessary ingredient. By taking into account finite-size corrections, for various types of boundary conditions we determine the universal Casimir force scaling function as a function of the scaling variable associated with the bulk field. Our numerical data are compared with analytic results obtained from mean-field theory.

cond-mat.stat-mech↗

arXiv2013

Critical Casimir torques and forces acting on needles in two spatial dimensions

We investigate the universal orientation-dependent interactions between non-spherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at bulk criticality. For a needle in an Ising strip the interaction on mesoscopic scales depends on the width of the strip and the length, position, and orientation of the needle. By lattice Monte Carlo simulations we evaluate the free energy difference between needle configurations being parallel and perpendicular to the strip. We concentrate on small but nonetheless mesoscopic needle lengths for which analytic predictions are available for comparison. All combinations of boundary conditions for the needles and boundaries are considered which belong to either the "normal" or the "ordinary" surface universality class, i.e., which induce local order or disorder, respectively. We also derive exact results for needles of arbitrary mesoscopic length, in particular for needles embedded in a half plane and oriented perpendicular to the corresponding boundary as well as for needles embedded at the center line of a symmetric strip with parallel orientation.

cond-mat.soft↗

arXiv2009

On scale-free and poly-scale behaviors of random hierarchical network

In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In particular, we compute numerically the spectral density of large random adjacency matrices defined by a hierarchy of the Bernoulli distributions $\{q_1,q_2,...\}$ on matrix elements, where $q_γ$ depends on hierarchy level $γ$ as $q_γ=p^{-μγ}$ ($μ>0$). For the spectral density we clearly see the free--scale behavior. We show also that for the Gaussian distributions on matrix elements with zero mean and variances $σ_γ=p^{-νγ}$, the tail of the spectral density, $ρ_G(λ)$, behaves as $ρ_G(λ) \sim |λ|^{-(2-ν)/(1-ν)}$ for $|λ|\to\infty$ and $0<ν<1$, while for $ν\ge 1$ the power--law behavior is terminated. We also find that the vertex degree distribution of such hierarchical networks has a poly--scale fractal behavior extended to a very broad range of scales.

cond-mat.dis-nn↗

arXiv2004

Topological percolation on a square lattice

We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the topological percolation threshold and the critical exponents of topological phase transition. Our numerical check confirms well obtained analytical results.

cond-mat.stat-mech↗

arXiv2000

Scaling of crossing probabilities for the q-state Potts model at criticality

We present study of finite-size scaling and universality of crossing probabilities for the $q$-state Potts model. Crossing probabilities of the Potts model are similar ones in percolation problem. We numerically investigated scaling of $π_{s}$ - the probability of a system to percolate only in one direction for two-dimensional site percolation, the Ising model, and the q-state Potts model for $q=3,4,5,6,8,10$. We found the thermal scaling index $y= \frac{1}ν$ for $q<4$. In contrast, $y \ne \frac{1}ν$ for $q=4$.

cond-mat.dis-nn↗

arXiv1998

Specific heat of two-dimensional diluted magnets

Using Monte Carlo techniques, the two-dimensional site-diluted Ising model is studied. In particular, properties of the specific heat, its critical behaviour and the emergence of a non-singular maximum above the transition temperature at moderate concentration of defects, are discussed.

cond-mat↗