arXiv subjects

V. I. Tokar

Publications and source records attributed to V. I. Tokar.

At least 19 recordsLinked to original sources

arXiv2025

Effective Hamiltonian approach to kinetic Ising models: Application to an infinitely long-range Husimi-Temperley model

The probability distribution (PD) of spin configurations in kinetic Ising models has been cast in the form of the canonical Boltzmann PD with a time-dependent effective Hamiltonian (EH). It has been argued that in systems with extensive energy EH depends linearly on the number of spins $N$ leading to the exponential dependence of PD on the system size. In macroscopic systems the argument of the exponential function may reach values of the order of the Avogadro number which is impossible to deal with computationally, thus making unusable the linear master equation (ME) governing the PD evolution. To overcome the difficulty, it has been suggested to use instead the nonlinear ME (NLME) for the EH density per spin. It has been shown that in spatially homogeneous systems NLME contains only terms of order unity even in the thermodynamic limit. The approach has been illustrated with the kinetic Husimi-Temperley model (HTM) evolving under the Glauber dynamics. At finite $ N $ the known numerical results has been reproduced and extended to broader parameter ranges. In the thermodynamic limit an exact nonlinear partial differential equation of the Hamilton-Jacobi type for EH has been derived. It has been shown that the average magnetization in HTM evolves according to the conventional kinetic mean field equation.

cond-mat.stat-mech↗

arXiv2025

Thinning algorithms for the Monte Carlo simulation of kinetic Ising models

The thinning method for numerical generation of the nonhomogeneous Poisson process (NHPP) arrival times has been adapted to accelerate Monte Carlo simulations of the kinetic Ising models (KIMs) with the Glauber spin-flip dynamics. The performance of the suggested algorithms has been illustrated by simulation of the decay of metastable states in stationary KIMs and of hysteresis in KIMs in a periodic external field. The thinning has been implemented by means of piecewise constant majorizing functions which exceed or are equal to NHPP rate. It has been shown that in favorable cases the use of thinning makes possible the simulations of hysteresis at frequencies in tens nanohertz and the decay of metastable states with lifetimes by many orders exceeding those in previous simulations. Good agreement of simulated results with low-temperature analytic theories has been established. Though the algorithm acceleration has been shown to enhance with lowering temperature, the hysteresis has been simulated at moderately low temperatures of practical interest estimated to cover the range from below the room temperature up to temperatures used in hyperthermia applications.

cond-mat.stat-mech↗

arXiv2023

Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation

The Wilson Green's function approach and, alternatively, Feynman's diffusion equation and the Hori representation have been used to derive an exact functional RG equation (EFRGE) that in the course of the RG flow interpolates between the interaction part of the lattice Ginzburg-Landau Hamiltonian and the logarithm of the generating functional of the S-matrix. Because the S-matrix vertices are the amputated correlation functions of the fluctuating field, it has been suggested that in the critical region the amputation of the long-range tails makes the S-matrix functional more localized and thus more amenable to the local potential approximation (LPA) than the renormalized free energy functional used in Wilson's EFRGE. By means of a functional Legendre transform the S-matrix EFRGE has been converted into an EFRGE for the effective action (EA). It has been found that the field-dependent part of EA predicted by the equation is the same as calculated within the known EA EFRGE approaches but in addition it is accurately accounts for the field-independent terms. These are indispensable in calculation of such important quantities as the the specific heat, the latent heat, etc. With the use of the derived EFRGE a closed expression for the renormalization counterterm has been obtained which when subtracted from the divergent solution of the Wetterich equation would lead to a finite exact expression for the EA thus making two approaches formally equivalent. The S-matrix equation has been found to be simply connected with a generalized functional Burgers' equation which establishes a direct correspondence between the first order phase transitions and the shock wave solutions of the RG equation. The transparent semi-group structure of the S-matrix RG equation makes possible the use of different RG techniques at different stages of the RG flow in order to improve the LPA solution.

cond-mat.stat-mech↗

arXiv2021

Renormalization group approach to unified description of continuous and the first order phase transitions: application to the Blume-Capel model

The renormalization group (RG) equation in the self-consistent local potential approximation (SC-LPA) suggested earlier for the description of continuous phase transitions in lattice models of the Landau-Ginzburg type has been applied to the solution of the spin-1 Blume-Capel model on the simple cubic lattice. The calculated transition temperatures of both continuous and the first-order phase transitions (FOPTs) in zero external field have been found to be in excellent agreement with the best available estimates. It has been argued that the SC-LPA RG equation may give more accurate and complete description of the FOPTs than those reported in alternative approaches. It has been shown that the SC-LPA RG equation can be cast in the form of the generalized Burgers' equation (GBE). In this formulation of the RG the FOPTs have been shown to assume the form of the shock-wave solutions of GBE in the inviscid limit. Universality of the RG flow in the vicinity of the fixed point describing FOPTs has been discussed.

cond-mat.stat-mech↗

arXiv2021

Self-consistent renormalization group approach to continuous phase transitions in alloys. Application to ordering in $β$-brass

A self-consistent (SC) renormalization group approach of the effective medium kind has been developed and applied to the solution of the Ising model (IM). A renormalization group equation in the local potential approximation (LPA) derived previously for spatially homogeneous systems has been extended to the lattice case and supplemented with a self-consistency condition on the pair correlation function. To validate the approach it has been applied to the simple cubic IM and good agreement of the spontaneous magnetization calculated with the use of the SC-LPA equation with the available exact Monte Carlo simulations data has been established. Next the approach has been applied to the bcc IM corresponding to $β$-brass. With the use of the effective pair interaction parameters from available {\em ab initio} calculations the critical temperature, the correlation length and the long range order parameter in the vicinity of the critical point have been calculated in excellent agreement with experimental data. Qualitative and quantitative arguments have been given in support of the suggestion that the experimentally observed decrease of the effective critical exponent of the order parameter in comparison with the universal value is enhanced by the positive value of the second neighbour pair interaction found in the {\em ab initio} calculations.

cond-mat.stat-mech↗

arXiv2019

Nonlocal diffusion currents at the nanoscale

An integro-differential expression for the diffusion current of the impurities diffusing by the mechanism of bound impurity-defect pairs has been derived. The ensuing nonlocal diffusion equation generalizes the existing theories of diffusion by the pair mechanism in unbounded systems with homogeneous defect distributions on the systems with boundaries and variable defect concentration. It has been established that the nonlocality manifests itself only at short diffusion times while at large times, in particular, under the stationary conditions, the predictions of the nonlocal theory would coincide with existing approaches based on local diffusion currents. Possibilities of experimental verification of the nonlocal theory have been suggested. In particular, the explanation of the uphill diffusion in silicon by the pair drag can be tested within slightly modified conventional experimental setups. Also, it has been shown that in the nonlocal theory the impurity segregation profile caused by the drag should differ at the initial stage of evolution from the predictions of the local theories. Because the segregation influences mechanical, corrosive, and electronic properties of materials, the nonlocal character of the pair diffusion may have important implications for nanostructured materials.

cond-mat.soft↗

arXiv2019

Effective medium approach in the renormalization group theory of phase transitions

An effective medium approach similar to the coherent potential approximation (CPA) in the theory of disordered alloys and to the DMFT has been extended to the renormalization group equations in the local potential approximation (LPA). Non-universal characteristics of the second order phase transitions such as the critical temperatures and critical amplitudes have been calculated in good agreement with the best known estimates. A possibility of cluster extension of the LPA to improve its accuracy and to make the approach systematic and self-contained has been discussed. A qualitative explanation of the discrepancy between theoretical value of the critical exponent $β$ and recent experimental data on ordering in beta brass by the influence of non-universal contributions has been suggested.

cond-mat.stat-mech↗

arXiv2019

Calculation of non-universal thermodynamic quantities within self-consistent non-perturbative functional renormalization group approach

A self-consistent renormalization scheme suitable for the calculation of non-universal quantities in $n$-vector models with pair spin interactions of arbitrary extent has been suggested. The method has been based on the elimination of the fluctuating field components within the layers defined by the layer-cake representation of the propagator. The non-perturbative renormalization group (RG) equations has been solved in the local potential approximation. Critical temperatures of the $n=1-3$ vector spin models on cubic lattices have been calculated in excellent agreement with the best known estimates. Several critical amplitudes and the magnetisation curve of the Ising model on the simple cubic lattice calculated within the approach compared well with the values from literature sources. It has been argued that unification of the method with cluster techniques would make possible the treatment of realistic lattice models with multi-spin interactions and describe in a unified framework the phase transitions of any kind. Besides the RG equations the layer-cake technique can be used in the exact partial renormalization of the local interactions in the functional lattice Hamiltonians. This procedure reduces the strength of the interactions which in some cases can make them amenable to perturbative treatment.

cond-mat.stat-mech↗

arXiv2018

Impurity Green's function in the five frequency model of diffusion in the FCC host: General case and the limit of strong impurity-vacancy binding

The impurity Green's function exact to the first order in the vacancy concentration has been calculated in the framework of the five frequency model (5FM). The solution in terms of determinant ratios has been obtained with the use of the Cramer's rule. The determinant sizes varied from 54 for the most general case to three for the four frequency model. Both analytical and numerical techniques has been used to analyze the solution. Special attention has been devoted to the case of strong impurity-vacancy (I-v) binding in order to substantiate the picture of diffusion via bound I-v pairs developed earlier in a phenomenological approach. Complete agreement with the phenomenological theory has been established thus providing its rigorous justification. The solution has been also applied to the calculation of the diffusional broadening of the Mössbauer resonance in FeAl system and good agreement with available experimental data and calculations within the encounter model has been found. The decay of the density of the nearest neighborI-v pairs has been discussed in detail and suggested to be used as an additional constraint on the parameters of the 5FM. The possibility of experimental observation of the decay with the use of the positron annihilation technique has been pointed out.

cond-mat.mtrl-sci↗

arXiv2018

Non-Gaussian diffusion profiles caused by mobile impurity-vacancy pairs in the five frequency model of diffusion

Vacancy-mediated diffusion of impurities under strong impurity-vacancy (I-v) attraction has been studied in the framework of the five-frequency model (5FM) for the FCC host. The system of impurities and tightly bound I-v pairs has been treated in the framework of the rate-equations approach of Cowern et al., Phys. Rev. Lett. 65, 2434 (1990), developed for the description of the non-Gaussian diffusion profiles (NGDPs) observed in dopant diffusion in silicon. In the present study this approach has been extended to derive a three-dimensional (3D) integro-differential equation describing the pair-mediated impurity diffusion. The equation predicts the same 1D NGDPs as in Cowern et al. but can be also used for the simulation of 3D profiles of arbitrary geometry in the systems where the diffusion proceeds via a mobile state. The parameters of the theory has been calculated within the 5FM on the basis of available literature data. The database on impurities in aluminum host has been analyzed and promising impurity-host systems for the observation of NGDPs has been identified. The diffusion profiles for an impurity where NGDPs are expected to be easily detectable have been simulated. It has been argued that with the input parameters calculated on the basis of experimental diffusion constants the simulated NGDPs can be accurate enough to serve as a quantitative test of the 5FM.

cond-mat.mtrl-sci↗

arXiv2016

Hybrid cluster+RG approach to the theory of phase transitions in strongly coupled Landau-Ginzburg-Wilson model

It is argued that cluster methods provide a viable alternative to Wilson's momentum shell integration technique at the early stage of renormalization in the field-theoretic models with strongly coupled fields because these methods allow for systematic accounting of all interactions in the system irrespective of their strength. These methods, however, are restricted to relatively small spatial scales, so they ought to be supplemented with more conventional renormalization-group (RG) techniques to account for large scale correlations. To fulfil this goal a "layer-cake" renormalization scheme earlier developed for rotationally symmetric Hamiltonians has been generalized to the lattice case. The RG technique can be naturally integrated with an appropriately modified cluster method so that the RG equations were used only in the presence of large scale fluctuations, while in their absence the approach reduced to a conventional cluster method. As an illustrative example the simplest single-site cluster approximation together with the local-potential RG equation are applied to simple cubic Ising model to calculate several non-universal quantities such as the magnetization curve, the critical temperature, and some critical amplitudes. Good agreement with Monte Carlo simulations and series expansion results was found.

cond-mat.stat-mech↗

arXiv2013

Rigorous derivation of the rate equations for the epitaxial growth

In the framework of the second-quantization representation of the master equation governing the irreversible epitaxial growth, exact equations describing the evolution of the island densities has been obtained. Their decoupling within a mean field-type approximation with the unknown correlation functions replaced by capture numbers (CNs) has been used to derive a closed set of rate equations. The latter has been compared with the exact equations to obtain rigorous definitions of the CNs. The CN that describes the nucleation of dimer islands from two mobile monomers has been measured in the exact kinetic Monte Carlo simulations with the use of the rigorous definition. Strong disagreement with the literature values calculated within alternative techniques has been found, especially at low surface coverage. Plausible causes for the discrepancies are suggested. Another important result of the rigorous approach is the rate equation with the term describing the monomer diffusion. The equation significantly differs from the widely used equations of this kind known from literature. Arguments in favour of our approach are given.

cond-mat.stat-mech↗

arXiv2010

Universality in adsorbate ordering on nanotube surfaces

Numerically efficient transfer matrix technique for studying statistics of coherent adsorbates on small nanotubes has been developed. In the framework of a realistic microscopic model fitted to the data of ab initio calculations taken from literature sources, the ordering of potassium adsorbate on (6,0) single-walled carbon nanotube has been studied. Special attention has been payed to the phase transition-like abrupt changes seen in the adsorption isotherms at low temperature. It has been found that the behavior during the transitions conforms with the universality hypothesis of the theory of critical phenomena and is qualitatively the same as in the one dimensional Ising model. Quantitatively the critical behavior can be fully described by two parameters. Their qualitative connection with the properties of interphase boundaries is suggested but further research is needed to develop a quantitative theory.

cond-mat.mes-hall↗

arXiv2010

Transfer matrix solution of the Wako-Saitô-Muñoz-Eaton model augmented by arbitrary short range interactions

The Wako-Sait{ô}-Muñoz-Eaton (WSME) model, initially introduced in the theory of protein folding, has also been used in modeling the RNA folding and some epitaxial phenomena. The advantage of this model is that it admits exact solution in the general inhomogeneous case (Bruscolini and Pelizzola, 2002) which facilitates the study of realistic systems. However, a shortcoming of the model is that it accounts only for interactions within continuous stretches of native bonds or atomic chains while neglecting interstretch (interchain) interactions. But due to the biopolymer (atomic chain) flexibility, the monomers (atoms) separated by several non-native bonds along the sequence can become closely spaced. This produces their strong interaction. The inclusion of non-WSME interactions into the model makes the model more realistic and improves its performance. In this study we add arbitrary interactions of finite range and solve the new model by means of the transfer matrix technique. We can therefore exactly account for the interactions which in proteomics are classified as medium- and moderately long-range ones.

cond-mat.mes-hall↗

arXiv2008

Perturbative calculation of non-local corrections to dynamical mean field theory

A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron correlation the one-electron Green's function is strongly spatially damped so that its intersite matrix elements may be considered as small perturbations. Because the non-local corrections are at least quadratic in these matrix elements, DMFT in such cases may be a very accurate approximation in dimensions d = 1-3. This observation provides a rigorous justification for the application of DMFT to physical systems. Furthermore, the technique allows for a systematic evaluation of the nonlocal corrections. This is illustrated with the calculation of the magnetic short range order parameter for nearest neighbor spins in the half filled Hubbard model on the square lattice in its insulating phase which exhibits an excellent agreement with the results of a recent cluster approach.As a second example we study the lowest order correction to the DMFT self-energy and its influence on the local density of states.

cond-mat.str-el↗

arXiv2008

Accelerated kinetic Monte Carlo algorithm for diffusion limited kinetics

If a stochastic system during some periods of its evolution can be divided into non-interacting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo algorithms. As an illustrative example the simulation of irreversible growth of extended one dimensional islands is considered. The new approach allowed to simulate the systems characterized by parameters superior to those used in previous simulations.

cond-mat.mtrl-sci↗

arXiv2005

Exact solution of the five frequency model of the vacancy-assisted impurity diffusion in the limit of vanishing vacancy concentration

The van Hove autocorrelation function of the impurity is obtained which is exact to the first order in the vacancy concentration. It is found that in the case of strong vacancy-impurity binding a singularity in the van Hove function corresponding to a resonant bound state develops on the unphysical sheet in the complex frequency plane close to the real axis. It is argued that this bound state corresponds to the defect-impurity pairs widely used in models of diffusion in semiconductors.

cond-mat.other↗

arXiv2002

Non-equilibrium gelation transition in a kinetic lattice gas model

We consider a lattice gas model which in addition to the canonical nearest neighbor pair interatomic interaction accounts for a many-body interaction inside atomic trios. Interactions of this kind arise in the coherent strained epitaxy and were recently used by us to describe some surface phenomena. With the use of the Monte Carlo simulation we show that in two dimensions the model at low temperature exhibits glassy behaviour, in particular, undergoes a gelation transition. We argue that this model may belong to the universality class of non-equilibrium critical phenomena which may comprise also some off-lattice structural glass transitions, provided such a class exists.

cond-mat.mtrl-sci↗